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Lu, Guozhen

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Author ID: lu.guozhen Recent zbMATH articles by "Lu, Guozhen"
Published as: Lu, G.; Lu, Guo Zhen; Lu, Guozhen
Homepage: https://www2.math.uconn.edu/~guozhenlu/
External Links: MGP · Wikidata · GND
Documents Indexed: 172 Publications since 1991, including 4 Books
all top 5

Serials

15 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
14 Advanced Nonlinear Studies
10 Acta Mathematica Sinica. English Series
9 Forum Mathematicum
9 Calculus of Variations and Partial Differential Equations
8 Revista Matemática Iberoamericana
8 The Journal of Geometric Analysis
7 Advances in Mathematics
7 Journal of Differential Equations
7 Journal of Functional Analysis
4 Indiana University Mathematics Journal
4 Transactions of the American Mathematical Society
4 Publicacions Matemàtiques
4 Potential Analysis
4 Communications on Pure and Applied Analysis
3 Communications in Partial Differential Equations
3 Discrete and Continuous Dynamical Systems
3 Mathematical Sciences Research Hot-Line
2 American Journal of Mathematics
2 Proceedings of the American Mathematical Society
2 Differential and Integral Equations
2 Mathematical Research Letters
2 Analysis & PDE
2 Advanced Lectures in Mathematics (ALM)
1 Analysis Mathematica
1 Communications on Pure and Applied Mathematics
1 Studia Mathematica
1 Annales de l’Institut Fourier
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 Bulletin of the London Mathematical Society
1 Bulletin de la Société Mathématique de France
1 Canadian Mathematical Bulletin
1 Journal of Approximation Theory
1 Mathematische Annalen
1 Mathematische Zeitschrift
1 Memoirs of the American Mathematical Society
1 Pacific Journal of Mathematics
1 Ricerche di Matematica
1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
1 Approximation Theory and its Applications
1 Constructive Approximation
1 International Journal of Mathematics
1 IMRN. International Mathematics Research Notices
1 Panamerican Mathematical Journal
1 Comptes Rendus de l’Académie des Sciences. Série I
1 Applied Mathematics. Series B (English Edition)
1 Electronic Journal of Differential Equations (EJDE)
1 Methods and Applications of Analysis
1 Electronic Research Announcements of the American Mathematical Society
1 The Journal of Fourier Analysis and Applications
1 Communications on Applied Nonlinear Analysis
1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique
1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
1 Nonlinear Analysis. Theory, Methods & Applications
1 Applied and Numerical Harmonic Analysis

Publications by Year

Citations contained in zbMATH Open

156 Publications have been cited 2,457 times in 1,091 Documents Cited by Year
Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates. Zbl 1232.42018
Hofmann, Steve; Lu, Guozhen; Mitrea, Dorina; Mitrea, Marius; Yan, Lixin
131
2011
Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander’s condition and applications. Zbl 0804.35015
Lu, Guozhen
82
1992
A new approach to sharp Moser-Trudinger and Adams type inequalities: a rearrangement-free argument. Zbl 1294.46034
Lam, Nguyen; Lu, Guozhen
68
2013
Existence and multiplicity of solutions to equations of \(N\)-Laplacian type with critical exponential growth in \(\mathbb R^N\). Zbl 1236.35050
Lam, Nguyen; Lu, Guozhen
68
2012
Best constants for Moser-Trudinger inequalities on the Heisenberg group. Zbl 1019.43009
Cohn, William S.; Lu, Guozhen
68
2001
Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications. Zbl 1278.42033
Lam, Nguyen; Lu, Guozhen
54
2012
Representation formulas and weighted Poincaré inequalities for Hörmander vector fields. Zbl 0820.46026
Franchi, Bruno; Lu, Guozhen; Wheeden, Richard L.
53
1995
The sharp Poincaré inequality for free vector fields: An endpoint result. Zbl 0860.35006
Lu, Guozhen
53
1994
Symmetry and regularity of extremals of an integral equation related to the Hardy-Sobolev inequality. Zbl 1231.35290
Lu, Guozhen; Zhu, Jiuyi
47
2011
Inhomogeneous infinity Laplace equation. Zbl 1152.35042
Lu, Guozhen; Wang, Peiyong
47
2008
Elliptic equations and systems with subcritical and critical exponential growth without the Ambrosetti-Rabinowitz condition. Zbl 1305.35069
Lam, Nguyen; Lu, Guozhen
46
2014
Convex functions on the Heisenberg group. Zbl 1072.49019
Lu, Guozhen; Manfredi, Juan J.; Stroffolini, Bianca
45
2004
A relationship between Poincaré-type inequalities and representation formulas in spaces of homogeneous type. Zbl 0856.43006
Franchi, Bruno; Lu, Guozhen; Wheeden, Richard L.
43
1996
Sharp constant and extremal function for the improved Moser-Trudinger inequality involving \(L^p\) norm in two dimension. Zbl 1182.35093
Lu, Guozhen; Yang, Yunyan
39
2009
Equivalence of critical and subcritical sharp Trudinger-Moser-Adams inequalities. Zbl 1387.46034
Lam, Nguyen; Lu, Guozhen; Zhang, Lu
37
2017
A PDE perspective of the normalized infinity Laplacian. Zbl 1157.35388
Lu, Guozhen; Wang, Peiyong
36
2008
Adams’ inequalities for bi-Laplacian and extremal functions in dimension four. Zbl 1172.46021
Lu, Guozhen; Yang, Yunyan
33
2009
Embedding theorems into Lipschitz and BMO spaces and applications to quasilinear subelliptic differential equations. Zbl 0873.35006
Lu, Guozhen
31
1996
Sharp constants for Moser-Trudinger inequalities on spheres in complex space \(\mathbb C^n\). Zbl 1063.35060
Cohn, William S.; Lu, Guozhen
29
2004
Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs. Zbl 1282.35393
Lam, Nguyen; Lu, Guozhen; Tang, Hanli
28
2014
An overdetermined problem in Riesz-potential and fractional Laplacian. Zbl 1236.31004
Lu, Guozhen; Zhu, Jiuyi
28
2012
Sharp Moser-Trudinger inequalities on hyperbolic spaces with exact growth condition. Zbl 1356.46031
Lu, Guozhen; Tang, Hanli
26
2016
\(N\)-Laplacian equations in \(\mathbb R^N\) with subcritical and critical growth without the Ambrosetti-Rabinowitz condition. Zbl 1283.35049
Lam, Nguyen; Lu, Guozhen
26
2013
Sharp Hardy-Adams inequalities for bi-Laplacian on hyperbolic space of dimension four. Zbl 1384.46026
Lu, Guozhen; Yang, Qiaohua
25
2017
Hörmander type theorems for multi-linear and multi-parameter Fourier multiplier operators with limited smoothness. Zbl 1286.42010
Chen, Jiao; Lu, Guozhen
25
2014
Best constants for Moser-Trudinger inequalities on high dimensional hyperbolic spaces. Zbl 1294.46035
Lu, Guozhen; Tang, Hanli
25
2013
Best constants and existence of maximizers for weighted Trudinger-Moser inequalities. Zbl 1364.46026
Dong, Mengxia; Lu, Guozhen
23
2016
Flag Hardy spaces and Marcinkiewicz multipliers on the Heisenberg group. Zbl 1318.42026
Han, Yongsheng; Lu, Guozhen; Sawyer, Eric
23
2014
Best constants for Moser-Trudinger inequalities, fundamental solutions and one-parameter representation formulas on groups of Heisenberg type. Zbl 1011.22004
Cohn, William S.; Lu, Guo Zhen
23
2002
Sharp weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg inequalities and their extremal functions. Zbl 1397.46027
Dong, Mengxia; Nguyen Lam; Lu, Guozhen
22
2018
Sharp constants and optimizers for a class of Caffarelli-Kohn-Nirenberg inequalities. Zbl 1367.26035
Lam, Nguyen; Lu, Guozhen
22
2017
Sharp Adams type inequalities in Sobolev spaces \(W^{m,\frac{n}{m}}(\mathbb R^n)\) for arbitrary integer \(m\). Zbl 1259.46029
Lam, Nguyen; Lu, Guozhen
22
2012
Sharp singular Adams inequalities in high order Sobolev spaces. Zbl 1319.46027
Nguyen Lam; Lu, Guozhen
21
2012
Polynomials, higher order Sobolev extension theorems and interpolation inequalities on weighted Folland-Stein spaces on stratified groups. Zbl 0973.46020
Lu, Guozhen
21
2000
Fourier analysis and optimal Hardy-Adams inequalities on hyperbolic spaces of any even dimension. Zbl 1402.46025
Li, Jungang; Lu, Guozhen; Yang, Qiaohua
20
2018
Characterization of balls in terms of Bessel-potential integral equation. Zbl 1229.31005
Han, Xiaolong; Lu, Guozhen; Zhu, Jiuyi
20
2012
Some equivalent definitions of high order Sobolev spaces on stratified groups and generalizations to metric spaces. Zbl 1007.46034
Liu, Yongping; Lu, Guozhen; Wheeden, Richard L.
20
2002
Existence and nonexistence of positive radial solutions for a class of semilinear elliptic systems. Zbl 0934.34011
Chen, Shaohua; Lu, Guozhen
20
1999
Existence of nontrivial solutions to polyharmonic equations with subcritical and critical exponential growth. Zbl 1245.35064
Lam, Nguyen; Lu, Guozhen
19
2012
Discrete Calderón’s identity, atomic decomposition and boundedness criterion of operators on multiparameter Hardy spaces. Zbl 1193.42090
Han, Y.; Lu, G.; Zhao, K.
19
2010
Convex functions on Carnot groups. Zbl 1124.49024
Juutinen, Petri; Lu, Guozhen; Manfredi, Juan J.; Stroffolini, Bianca
19
2007
Concentration-compactness principle for Trudinger-Moser inequalities on Heisenberg groups and existence of ground state solutions. Zbl 1402.46026
Li, Jungang; Lu, Guozhen; Zhu, Maochun
18
2018
A sharp Trudinger-Moser inequality on any bounded and convex planar domain. Zbl 1369.46029
Lu, Guozhen; Yang, Qiaohua
18
2016
Multiparameter Hardy space theory on Carnot-Carathéodory spaces and product spaces of homogeneous type. Zbl 1275.42035
Han, Yongsheng; Li, Ji; Lu, Guozhen
18
2013
Boundedness of singular integrals on multiparameter weighted Hardy spaces \(H^p_w(\mathbb R^n \times \mathbb R^m)\). Zbl 1271.42017
Ding, Yong; Han, Yongsheng; Lu, Guozhen; Wu, Xinfeng
18
2012
Axial symmetry and regularity of solutions to an integral equation in a half-space. Zbl 1239.45005
Lu, Guozhen; Zhu, Jiuyi
18
2011
Duality of multiparameter Hardy spaces \(H^{p}\) on spaces of homogeneous type. Zbl 1213.42073
Han, Yongsheng; Li, Ji; Lu, Guozhen
18
2010
Infinity Laplace equation with non-trivial right-hand side. Zbl 1194.35194
Lu, Guozhen; Wang, Peiyong
18
2010
On nonuniformly subelliptic equations of \(Q\)-sub-Laplacian type with critical growth in the Heisenberg group. Zbl 1282.35139
Lam, Nguyen; Lu, Guozhen; Tang, Hanli
17
2012
Sharp affine and improved Moser-Trudinger-Adams type inequalities on unbounded domains in the spirit of Lions. Zbl 1372.46027
Lam, Nguyen; Lu, Guozhen; Tang, Hanli
16
2017
Sharp singular Trudinger-Moser inequalities in Lorentz-Sobolev spaces. Zbl 1359.46035
Lu, Guozhen; Tang, Hanli
16
2016
Best constants for Adams’ inequalities with the exact growth condition in \({\mathbb R}^n\). Zbl 1352.46034
Lu, Guozhen; Tang, Hanli; Zhu, Maochun
16
2015
\(L^p\) estimates for multi-linear and multi-parameter pseudo-differential operators. Zbl 1335.47033
Dai, Wei; Lu, Guozhen
16
2015
Multilinear Calderón-Zygmund operators with kernels of Dini’s type and applications. Zbl 1290.42039
Lu, Guozhen; Zhang, Pu
16
2014
Multi-parameter Triebel-Lizorkin and Besov spaces associated with flag singular integrals. Zbl 1192.42014
Ding, Yong; Lu, Guo Zhen; Ma, Bo Lin
16
2010
Boman equals John. Zbl 0861.43007
Buckley, S.; Koskela, P.; Lu, Guozhen
16
1996
Weighted Poincaré inequalities for Hörmander vector fields and local regularity for a class of degenerate elliptic equations. Zbl 0841.46018
Franchi, B.; Lu, G.; Wheeden, R. L.
16
1995
Hardy-Littlewood-Sobolev and Stein-Weiss inequalities and integral systems on the Heisenberg group. Zbl 1309.42032
Han, Xiaolong; Lu, Guozhen; Zhu, Jiuyi
15
2012
Some recent works on multiparameter Hardy space theory and discrete Littlewood-Paley analysis. Zbl 1201.42016
Han, Yongsheng; Lu, Guozhen
15
2010
Singular integrals and commutators on homogeneous groups. Zbl 1026.43007
Lu, Guozhen; Lu, Shanzhen; Yang, Dachun
15
2002
Embedding theorems on Campanato-Morrey spaces for vector fields of Hörmander type. Zbl 0916.46026
Lu, Guozhen
15
1998
Local and global interpolation inequalities on the Folland-Stein Sobolev spaces and polynomials on stratified groups. Zbl 0910.26007
Lu, Guozhen
15
1997
A Fefferman-Phong type inequality for degenerate vector fields and applications. Zbl 0878.35050
Lu, Guozhen
15
1996
Paneitz operators on hyperbolic spaces and high order Hardy-Sobolev-Maz’ya inequalities on half spaces. Zbl 1431.26013
Lu, Guozhen; Yang, Qiaohua
14
2019
High order representation formulas and embedding theorems on stratified groups and generalizations. Zbl 0974.46039
Lu, Guozhen; Wheeden, Richard L.
14
2000
On Harnack’s inequality for a class of strongly degenerate Schrödinger operators formed by vector fields. Zbl 0827.35032
Lu, Guozhen
14
1994
Sharpened Adams inequality and ground state solutions to the bi-Laplacian equation in \(\mathbb{R}^4\). Zbl 1397.35097
Chen, Lu; Li, Jungang; Lu, Guozhen; Zhang, Caifeng
13
2018
Symbolic calculus and boundedness of multi-parameter and multi-linear pseudo-differential operators. Zbl 1321.47111
Hong, Qing; Lu, Guozhen
13
2014
Duality theory of weighted Hardy spaces with arbitrary number of parameters. Zbl 1298.42025
Lu, Guozhen; Ruan, Zhuoping
13
2014
Hardy spaces associated with different homogeneities and boundedness of composition operators. Zbl 1291.42018
Han, Yongsheng; Lin, Chincheng; Lu, Guozhen; Ruan, Zhuoping; Sawyer, Eric T.
13
2013
Boundedness criterion of Journé’s class of singular integrals on multiparameter Hardy spaces. Zbl 1268.42024
Han, Yongsheng; Lu, Guozhen; Ruan, Zhuoping
13
2013
An optimal representation formula for Carnot-Carathéodory vector fields. Zbl 0931.31003
Lu, Guozhen; Wheeden, Richard L.
13
1998
Embedding theorems on Campanato-Morrey spaces for vector fields and applications. Zbl 0842.46019
Lu, Guozhen
13
1995
Existence and size estimates for the Green’s functions of differential operators constructed from degenerate vector fields. Zbl 0798.35002
Lu, Guozhen
13
1992
Existence and nonexistence of extremal functions for sharp Trudinger-Moser inequalities. Zbl 1421.35008
Lam, Nguyen; Lu, Guozhen; Zhang, Lu
12
2019
\(L^{p}\) boundedness of rough bi-parameter Fourier integral operators. Zbl 1381.42024
Hong, Qing; Lu, Guozhen; Zhang, Lu
12
2018
Liouville type theorems for PDE and IE systems involving fractional Laplacian on a half space. Zbl 1364.35421
Dai, Wei; Liu, Zhao; Lu, Guozhen
12
2017
The Moser-Trudinger and Adams inequalities and elliptic and subelliptic equations with nonlinearity of exponential growth. Zbl 1317.35018
Lam, Nguyen; Lu, Guozhen
12
2012
Sub-elliptic global high order Poincaré inequalities in stratified Lie groups and applications. Zbl 1129.22007
Cohn, William S.; Lu, Guozhen; Wang, Peiyong
12
2007
Simultaneous representation and approximation formulas and high-order Sobolev embedded theorems on stratified groups. Zbl 1070.46024
Lu, Guozhen; Wheeden, Richard L.
12
2004
On positive entire solutions to the Yamabe-type problem on the Heisenberg and stratified groups. Zbl 0887.35052
Lu, Guozhen; Wei, Juncheng
12
1997
Duality of multi-parameter Triebel-Lizorkin spaces associated with the composition of two singular integral operators. Zbl 1338.42025
Ding, Wei; Lu, Guozhen
11
2016
Bounds of singular integrals on weighted Hardy spaces and discrete Littlewood-Paley analysis. Zbl 1408.42009
Lu, Guozhen; Zhu, Yueping
11
2012
Regularity of solutions to an integral equation associated with Bessel potential. Zbl 1237.45002
Han, Xiaolong; Lu, Guozhen
11
2011
A sharpened Moser-Pohozaev-Trudinger inequality with mean value zero in \(\mathbb R^2\). Zbl 1179.58010
Lu, Guozhen; Yang, Yunyan
11
2009
A sharp Trudinger-Moser type inequality involving \(L^n\) norm in the entire space \(\mathbb{R}^n\). Zbl 1432.35081
Lu, Guozhen; Zhu, Maochun
10
2019
The Moser-Trudinger inequality in unbounded domains of Heisenberg group and sub-elliptic equations. Zbl 1254.35063
Cohn, William S.; Lam, Nguyen; Lu, Guozhen; Yang, Yunyan
10
2012
On a Sobolev inequality with remainder terms. Zbl 0961.35100
Lu, Guozhen; Wei, Juncheng
10
2000
Multi-parameter local Hardy spaces. Zbl 1418.42038
Ding, Wei; Lu, Guozhen; Zhu, YuePing
9
2019
Singular integrals and weighted Triebel-Lizorkin and Besov spaces of arbitrary number of parameters. Zbl 1261.42030
Lu, Guo Zhen; Zhu, Yue Ping
9
2013
Factorizations and Hardy’s type identities and inequalities on upper half spaces. Zbl 1435.26015
Lam, Nguyen; Lu, Guozhen; Zhang, Lu
8
2019
Symmetry and regularity of solutions to the weighted Hardy-Sobolev type system. Zbl 1382.35326
Chen, Lu; Liu, Zhao; Lu, Guozhen
8
2016
Boundedness of multi-parameter Fourier multiplier operators on Triebel-Lizorkin and Besov-Lipschitz spaces. Zbl 1333.42013
Chen, Lu; Lu, Guozhen; Luo, Xiang
8
2016
Boundedness of singular integrals in Journé’s class on weighted multiparameter Hardy spaces. Zbl 1302.42024
Han, Yongsheng; Lu, Guozhen; Ruan, Zhuoping
8
2014
Liouville-type theorems and decay estimates for solutions to higher order elliptic equations. Zbl 1255.35064
Lu, Guozhen; Wang, Peiyong; Zhu, Jiuyi
8
2012
\(H^p\to H^p\) boundedness implies \(H^p\to L^p\) boundedness. Zbl 1225.42014
Han, Yongsheng; Li, Ji; Lu, Guozhen; Wang, Peiyong
8
2011
A uniqueness theorem for degenerate elliptic equations. Zbl 1187.35109
Lu, Guozhen; Wang, Peiyong
8
2008
On nonlinear Schrödinger equations with totally degenerate potentials. Zbl 0911.35047
Lu, Guozhen; Wei, Juncheng
8
1998
Weighted \(L^{p}\) estimates for rough bi-parameter Fourier integral operators. Zbl 1401.42013
Hong, Qing; Lu, Guozhen
7
2018
Multi-parameter Triebel-Lizorkin spaces associated with the composition of two singular integrals and their atomic decomposition. Zbl 1335.42021
Ding, Wei; Lu, Guozhen; Zhu, Yueping
7
2016
Geometric Hardy’s inequalities with general distance functions. Zbl 07235744
Lam, Nguyen; Lu, Guozhen; Zhang, Lu
5
2020
Sharp Adams and Hardy-Adams inequalities of any fractional order on hyperbolic spaces of all dimensions. Zbl 1451.46036
Li, Jungang; Lu, Guozhen; Yang, Qiaohua
5
2020
Boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces. Zbl 1442.42054
Chen, Jiao; Ding, Wei; Lu, Guozhen
1
2020
Boundedness of inhomogeneous Journé’s type operators on multi-parameter local Hardy spaces. Zbl 1440.42052
Ding, Wei; Lu, Guozhen
1
2020
Existence and nonexistence of extremals for critical Adams inequalities in \(\mathbb{R}^4\) and Trudinger-Moser inequalities in \(\mathbb{R}^2\). Zbl 1441.35121
Chen, Lu; Lu, Guozhen; Zhu, Maochun
1
2020
Paneitz operators on hyperbolic spaces and high order Hardy-Sobolev-Maz’ya inequalities on half spaces. Zbl 1431.26013
Lu, Guozhen; Yang, Qiaohua
14
2019
Existence and nonexistence of extremal functions for sharp Trudinger-Moser inequalities. Zbl 1421.35008
Lam, Nguyen; Lu, Guozhen; Zhang, Lu
12
2019
A sharp Trudinger-Moser type inequality involving \(L^n\) norm in the entire space \(\mathbb{R}^n\). Zbl 1432.35081
Lu, Guozhen; Zhu, Maochun
10
2019
Multi-parameter local Hardy spaces. Zbl 1418.42038
Ding, Wei; Lu, Guozhen; Zhu, YuePing
9
2019
Factorizations and Hardy’s type identities and inequalities on upper half spaces. Zbl 1435.26015
Lam, Nguyen; Lu, Guozhen; Zhang, Lu
8
2019
Sharp singular Trudinger-Moser inequalities under different norms. Zbl 1421.35007
Lam, Nguyen; Lu, Guozhen; Zhang, Lu
6
2019
Sharp weighted Trudinger-Moser-Adams inequalities on the whole space and the existence of their extremals. Zbl 1421.35099
Chen, Lu; Lu, Guozhen; Zhang, Caifeng
5
2019
Discrete Littlewood-Paley-Stein characterization of multi-parameter local Hardy spaces. Zbl 1440.42104
Ding, Wei; Lu, Guozhen; Zhu, Yueping
4
2019
Existence of extremal functions for the Stein-Weiss inequalities on the Heisenberg group. Zbl 1429.26034
Chen, Lu; Lu, Guozhen; Tao, Chunxia
4
2019
Hardy-Littlewood-Sobolev inequalities with the fractional Poisson kernel and their applications in PDEs. Zbl 1418.35008
Chen, Lu; Lu, Guozhen; Tao, Chunxia
2
2019
Reverse Stein-Weiss inequalities on the upper half space and the existence of their extremals. Zbl 1422.42036
Chen, Lu; Lu, Guozhen; Tao, Chunxia
1
2019
Sharp maximal estimates for multilinear commutators of multilinear strongly singular Calderón-Zygmund operators and applications. Zbl 1409.42011
Lin, Yan; Lu, Guozhen; Lu, Shanzhen
1
2019
Sharp weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg inequalities and their extremal functions. Zbl 1397.46027
Dong, Mengxia; Nguyen Lam; Lu, Guozhen
22
2018
Fourier analysis and optimal Hardy-Adams inequalities on hyperbolic spaces of any even dimension. Zbl 1402.46025
Li, Jungang; Lu, Guozhen; Yang, Qiaohua
20
2018
Concentration-compactness principle for Trudinger-Moser inequalities on Heisenberg groups and existence of ground state solutions. Zbl 1402.46026
Li, Jungang; Lu, Guozhen; Zhu, Maochun
18
2018
Sharpened Adams inequality and ground state solutions to the bi-Laplacian equation in \(\mathbb{R}^4\). Zbl 1397.35097
Chen, Lu; Li, Jungang; Lu, Guozhen; Zhang, Caifeng
13
2018
\(L^{p}\) boundedness of rough bi-parameter Fourier integral operators. Zbl 1381.42024
Hong, Qing; Lu, Guozhen; Zhang, Lu
12
2018
Weighted \(L^{p}\) estimates for rough bi-parameter Fourier integral operators. Zbl 1401.42013
Hong, Qing; Lu, Guozhen
7
2018
Hörmander type theorem on bi-parameter Hardy spaces for bi-parameter Fourier multipliers with optimal smoothness. Zbl 1422.42023
Chen, Jiao; Lu, Guozhen
6
2018
Reverse Stein-Weiss inequalities and existence of their extremal functions. Zbl 1418.42041
Chen, Lu; Liu, Zhao; Lu, Guozhen; Tao, Chunxia
5
2018
Weighted Moser-Onofri-Beckner and logarithmic Sobolev inequalities. Zbl 1392.26029
Lam, Nguyen; Lu, Guozhen
3
2018
Equivalence of critical and subcritical sharp Trudinger-Moser-Adams inequalities. Zbl 1387.46034
Lam, Nguyen; Lu, Guozhen; Zhang, Lu
37
2017
Sharp Hardy-Adams inequalities for bi-Laplacian on hyperbolic space of dimension four. Zbl 1384.46026
Lu, Guozhen; Yang, Qiaohua
25
2017
Sharp constants and optimizers for a class of Caffarelli-Kohn-Nirenberg inequalities. Zbl 1367.26035
Lam, Nguyen; Lu, Guozhen
22
2017
Sharp affine and improved Moser-Trudinger-Adams type inequalities on unbounded domains in the spirit of Lions. Zbl 1372.46027
Lam, Nguyen; Lu, Guozhen; Tang, Hanli
16
2017
Liouville type theorems for PDE and IE systems involving fractional Laplacian on a half space. Zbl 1364.35421
Dai, Wei; Liu, Zhao; Lu, Guozhen
12
2017
Hardy-Sobolev type integral systems with Dirichlet boundary conditions in a half space. Zbl 1369.45005
Dai, Wei; Liu, Zhao; Lu, Guozhen
5
2017
\(\mathrm{L}^p\) estimates for a trilinear pseudo-differential operator with flag symbols. Zbl 1371.42012
Lu, Guozhen; Zhang, Lu
4
2017
Sharp Moser-Trudinger inequalities on hyperbolic spaces with exact growth condition. Zbl 1356.46031
Lu, Guozhen; Tang, Hanli
26
2016
Best constants and existence of maximizers for weighted Trudinger-Moser inequalities. Zbl 1364.46026
Dong, Mengxia; Lu, Guozhen
23
2016
A sharp Trudinger-Moser inequality on any bounded and convex planar domain. Zbl 1369.46029
Lu, Guozhen; Yang, Qiaohua
18
2016
Sharp singular Trudinger-Moser inequalities in Lorentz-Sobolev spaces. Zbl 1359.46035
Lu, Guozhen; Tang, Hanli
16
2016
Duality of multi-parameter Triebel-Lizorkin spaces associated with the composition of two singular integral operators. Zbl 1338.42025
Ding, Wei; Lu, Guozhen
11
2016
Symmetry and regularity of solutions to the weighted Hardy-Sobolev type system. Zbl 1382.35326
Chen, Lu; Liu, Zhao; Lu, Guozhen
8
2016
Boundedness of multi-parameter Fourier multiplier operators on Triebel-Lizorkin and Besov-Lipschitz spaces. Zbl 1333.42013
Chen, Lu; Lu, Guozhen; Luo, Xiang
8
2016
Multi-parameter Triebel-Lizorkin spaces associated with the composition of two singular integrals and their atomic decomposition. Zbl 1335.42021
Ding, Wei; Lu, Guozhen; Zhu, Yueping
7
2016
Bi-parameter and bilinear Calderón-Vaillancourt theorem with subcritical order. Zbl 1351.42028
Lu, Guozhen; Zhang, Lu
6
2016
Polyharmonic equations with critical exponential growth in the whole space \(\mathbb{R}^{n}\). Zbl 1323.35046
Lu, Guozhen; Lam, Nguyen; Bao, Jiguang
6
2016
Hardy space estimates for Littlewood-Paley-Stein square functions and Calderón-Zygmund operators. Zbl 1337.42019
Hart, Jarod; Lu, Guozhen
4
2016
Hardy space estimates for bilinear square functions and Calderón-Zygmund operators. Zbl 1358.42012
Hart, Jarod; Lu, Guozhen
1
2016
Best constants for Adams’ inequalities with the exact growth condition in \({\mathbb R}^n\). Zbl 1352.46034
Lu, Guozhen; Tang, Hanli; Zhu, Maochun
16
2015
\(L^p\) estimates for multi-linear and multi-parameter pseudo-differential operators. Zbl 1335.47033
Dai, Wei; Lu, Guozhen
16
2015
The maximum principles and symmetry results for viscosity solutions of fully nonlinear equations. Zbl 1312.35033
Lu, Guozhen; Zhu, Jiuyi
7
2015
Sharp singular Trudinger-Moser-Adams type inequalities with exact growth. Zbl 1338.35016
Lam, Nguyen; Lu, Guozhen
4
2015
Poincaré and Sobolev inequalities for vector fields satisfying Hörmander’s condition in variable exponent Sobolev spaces. Zbl 1339.46033
Li, Xia; Lu, Guo Zhen; Tang, Han Li
4
2015
Characterizations of second order Sobolev spaces. Zbl 1339.46030
Cui, Xiaoyue; Lam, Nguyen; Lu, Guozhen
2
2015
\(L^p\) estimates for bilinear and multiparameter Hilbert transforms. Zbl 1329.42008
Dai, Wei; Lu, Guozhen
1
2015
Elliptic equations and systems with subcritical and critical exponential growth without the Ambrosetti-Rabinowitz condition. Zbl 1305.35069
Lam, Nguyen; Lu, Guozhen
46
2014
Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs. Zbl 1282.35393
Lam, Nguyen; Lu, Guozhen; Tang, Hanli
28
2014
Hörmander type theorems for multi-linear and multi-parameter Fourier multiplier operators with limited smoothness. Zbl 1286.42010
Chen, Jiao; Lu, Guozhen
25
2014
Flag Hardy spaces and Marcinkiewicz multipliers on the Heisenberg group. Zbl 1318.42026
Han, Yongsheng; Lu, Guozhen; Sawyer, Eric
23
2014
Multilinear Calderón-Zygmund operators with kernels of Dini’s type and applications. Zbl 1290.42039
Lu, Guozhen; Zhang, Pu
16
2014
Symbolic calculus and boundedness of multi-parameter and multi-linear pseudo-differential operators. Zbl 1321.47111
Hong, Qing; Lu, Guozhen
13
2014
Duality theory of weighted Hardy spaces with arbitrary number of parameters. Zbl 1298.42025
Lu, Guozhen; Ruan, Zhuoping
13
2014
Boundedness of singular integrals in Journé’s class on weighted multiparameter Hardy spaces. Zbl 1302.42024
Han, Yongsheng; Lu, Guozhen; Ruan, Zhuoping
8
2014
New characterizations of Sobolev spaces on the Heisenberg group. Zbl 1316.46033
Cui, Xiaoyue; Lam, Nguyen; Lu, Guozhen
3
2014
A new approach to sharp Moser-Trudinger and Adams type inequalities: a rearrangement-free argument. Zbl 1294.46034
Lam, Nguyen; Lu, Guozhen
68
2013
\(N\)-Laplacian equations in \(\mathbb R^N\) with subcritical and critical growth without the Ambrosetti-Rabinowitz condition. Zbl 1283.35049
Lam, Nguyen; Lu, Guozhen
26
2013
Best constants for Moser-Trudinger inequalities on high dimensional hyperbolic spaces. Zbl 1294.46035
Lu, Guozhen; Tang, Hanli
25
2013
Multiparameter Hardy space theory on Carnot-Carathéodory spaces and product spaces of homogeneous type. Zbl 1275.42035
Han, Yongsheng; Li, Ji; Lu, Guozhen
18
2013
Hardy spaces associated with different homogeneities and boundedness of composition operators. Zbl 1291.42018
Han, Yongsheng; Lin, Chincheng; Lu, Guozhen; Ruan, Zhuoping; Sawyer, Eric T.
13
2013
Boundedness criterion of Journé’s class of singular integrals on multiparameter Hardy spaces. Zbl 1268.42024
Han, Yongsheng; Lu, Guozhen; Ruan, Zhuoping
13
2013
Singular integrals and weighted Triebel-Lizorkin and Besov spaces of arbitrary number of parameters. Zbl 1261.42030
Lu, Guo Zhen; Zhu, Yue Ping
9
2013
Characterizations of Sobolev spaces in Euclidean spaces and Heisenberg groups. Zbl 1299.46032
Cui, Xiaoyue; Lam, Nguyen; Lu, Guozhen
6
2013
Liouville-type theorems for fully nonlinear elliptic equations and systems in half spaces. Zbl 1298.35021
Lu, Guozhen; Zhu, Jiuyi
3
2013
Existence and multiplicity of solutions to equations of \(N\)-Laplacian type with critical exponential growth in \(\mathbb R^N\). Zbl 1236.35050
Lam, Nguyen; Lu, Guozhen
68
2012
Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications. Zbl 1278.42033
Lam, Nguyen; Lu, Guozhen
54
2012
An overdetermined problem in Riesz-potential and fractional Laplacian. Zbl 1236.31004
Lu, Guozhen; Zhu, Jiuyi
28
2012
Sharp Adams type inequalities in Sobolev spaces \(W^{m,\frac{n}{m}}(\mathbb R^n)\) for arbitrary integer \(m\). Zbl 1259.46029
Lam, Nguyen; Lu, Guozhen
22
2012
Sharp singular Adams inequalities in high order Sobolev spaces. Zbl 1319.46027
Nguyen Lam; Lu, Guozhen
21
2012
Characterization of balls in terms of Bessel-potential integral equation. Zbl 1229.31005
Han, Xiaolong; Lu, Guozhen; Zhu, Jiuyi
20
2012
Existence of nontrivial solutions to polyharmonic equations with subcritical and critical exponential growth. Zbl 1245.35064
Lam, Nguyen; Lu, Guozhen
19
2012
Boundedness of singular integrals on multiparameter weighted Hardy spaces \(H^p_w(\mathbb R^n \times \mathbb R^m)\). Zbl 1271.42017
Ding, Yong; Han, Yongsheng; Lu, Guozhen; Wu, Xinfeng
18
2012
On nonuniformly subelliptic equations of \(Q\)-sub-Laplacian type with critical growth in the Heisenberg group. Zbl 1282.35139
Lam, Nguyen; Lu, Guozhen; Tang, Hanli
17
2012
Hardy-Littlewood-Sobolev and Stein-Weiss inequalities and integral systems on the Heisenberg group. Zbl 1309.42032
Han, Xiaolong; Lu, Guozhen; Zhu, Jiuyi
15
2012
The Moser-Trudinger and Adams inequalities and elliptic and subelliptic equations with nonlinearity of exponential growth. Zbl 1317.35018
Lam, Nguyen; Lu, Guozhen
12
2012
Bounds of singular integrals on weighted Hardy spaces and discrete Littlewood-Paley analysis. Zbl 1408.42009
Lu, Guozhen; Zhu, Yueping
11
2012
The Moser-Trudinger inequality in unbounded domains of Heisenberg group and sub-elliptic equations. Zbl 1254.35063
Cohn, William S.; Lam, Nguyen; Lu, Guozhen; Yang, Yunyan
10
2012
Liouville-type theorems and decay estimates for solutions to higher order elliptic equations. Zbl 1255.35064
Lu, Guozhen; Wang, Peiyong; Zhu, Jiuyi
8
2012
Dual spaces of weighted multi-parameter Hardy spaces associated with the Zygmund dilation. Zbl 1275.42031
Han, Xiaolong; Lu, Guozhen; Xiao, Yayuan
4
2012
Atomic decomposition and boundedness criterion of operators on multi-parameter Hardy spaces of homogeneous type. Zbl 1258.42021
Lu, Guo Zhen; Xiao, Ya Yuan
4
2012
On regularity of solutions to an integral system associated with Bessel potentials. Zbl 1245.45002
Han, Xiaolong; Lu, Guozhen
2
2012
Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates. Zbl 1232.42018
Hofmann, Steve; Lu, Guozhen; Mitrea, Dorina; Mitrea, Marius; Yan, Lixin
131
2011
Symmetry and regularity of extremals of an integral equation related to the Hardy-Sobolev inequality. Zbl 1231.35290
Lu, Guozhen; Zhu, Jiuyi
47
2011
Axial symmetry and regularity of solutions to an integral equation in a half-space. Zbl 1239.45005
Lu, Guozhen; Zhu, Jiuyi
18
2011
Regularity of solutions to an integral equation associated with Bessel potential. Zbl 1237.45002
Han, Xiaolong; Lu, Guozhen
11
2011
\(H^p\to H^p\) boundedness implies \(H^p\to L^p\) boundedness. Zbl 1225.42014
Han, Yongsheng; Li, Ji; Lu, Guozhen; Wang, Peiyong
8
2011
A geometric covering lemma and nodal sets of eigenfunctions. Zbl 1244.58013
Han, Xiaolong; Lu, Guozhen
1
2011
Discrete Calderón’s identity, atomic decomposition and boundedness criterion of operators on multiparameter Hardy spaces. Zbl 1193.42090
Han, Y.; Lu, G.; Zhao, K.
19
2010
Duality of multiparameter Hardy spaces \(H^{p}\) on spaces of homogeneous type. Zbl 1213.42073
Han, Yongsheng; Li, Ji; Lu, Guozhen
18
2010
Infinity Laplace equation with non-trivial right-hand side. Zbl 1194.35194
Lu, Guozhen; Wang, Peiyong
18
2010
Multi-parameter Triebel-Lizorkin and Besov spaces associated with flag singular integrals. Zbl 1192.42014
Ding, Yong; Lu, Guo Zhen; Ma, Bo Lin
16
2010
Some recent works on multiparameter Hardy space theory and discrete Littlewood-Paley analysis. Zbl 1201.42016
Han, Yongsheng; Lu, Guozhen
15
2010
On the uniqueness of a solution of a two-phase free boundary problem. Zbl 1185.35340
Lu, Guozhen; Wang, Peiyong
5
2010
Sharp constant and extremal function for the improved Moser-Trudinger inequality involving \(L^p\) norm in two dimension. Zbl 1182.35093
Lu, Guozhen; Yang, Yunyan
39
2009
...and 56 more Documents
all top 5

Cited by 1,024 Authors

92 Lu, Guozhen
41 Yang, Dachun
27 Lam, Nguyen
27 Li, Ji
25 Duong, Xuan Thinh
23 Niu, Pengcheng
20 Yan, Lixin
19 Nguyễn Văn Hoàng
19 Yang, Qiaohua
18 Franchi, Bruno
17 Chen, Lu
16 Do Ó, João M. Bezerra
16 Yang, Yunyan
15 Song, Liang
14 Wang, Jialin
14 Yang, Sibei
13 Bui, The Anh
12 Han, Yongsheng
12 Zhu, Maochun
11 Bonfiglioli, Andrea
11 Chen, Wenxiong
11 de Souza, Manassés
11 Manfredi, Juan J.
11 Wu, Xinfeng
10 Ding, Wei
10 Lanconelli, Ermanno
10 Liao, Dongni
10 Wheeden, Richard Lee
9 Cao, Jun
9 Guliyev, Vagif Sabir
9 Liu, Yu
9 Tang, Hanli
9 Uguzzoni, Francesco
8 Chen, Jiao
8 Chua, Seng-Kee
8 Dai, Wei
8 Li, Congming
8 Sani, Federica
8 Yang, Xiaoping
8 Zhu, Jiuyi
8 Zhu, Yueping
7 Aouaoui, Sami
7 Capogna, Luca
7 Chang, Der-Chen E.
7 Dou, Jingbo
7 Dziubański, Jacek
7 Garofalo, Nicola
7 Liu, Fang
7 Liu, Zhao
7 Morbidelli, Daniele
7 Tan, Chaoqiang
7 Yang, Zuodong
7 Zhang, Caifeng
7 Zhang, Lu
7 Zhu, Xiaobao
6 Baldi, Annalisa
6 Chen, Peng
6 Crasta, Graziano
6 Di Fazio, Giuseppe
6 Ferrari, Fausto
6 Fragalà, Ilaria
6 Fu, Zunwei
6 Gong, Ruming
6 Han, Yanchang
6 Han, Yazhou
6 Huang, Jizheng
6 Li, Pengtao
6 Liu, Suying
6 Liu, Zhao
6 Mohammed, Ahmed
6 Montanari, Annamaria
6 Rossi, Julio Daniel
6 Sreenadh, Konijeti
6 Vodop’yanov, Sergeĭ Konstantinovich
6 Wang, Peiyong
6 Wick, Brett D.
6 Yang, Dongyong
6 Yuan, Wen
6 Zamboni, Pietro
5 Balogh, Zoltán M.
5 Bieske, Thomas J.
5 Citti, Giovanna
5 Dragoni, Federica
5 Fanciullo, Maria Stella
5 Giacomoni, Jacques
5 Gutiérrez, Cristian E.
5 Huang, Liang
5 Liang, YiYu
5 Lin, Yan
5 Lu, Shanzhen
5 Maldonado, Diego
5 Mishra, Pawan Kumar
5 Monti, Roberto
5 Nguyen Tuan Duy
5 Ruzhansky, Michael V.
5 Shi, Shaoguang
5 Sun, Mingbao
5 Tao, Chunxia
5 Tyson, Jeremy T.
5 Wang, Xumin
...and 924 more Authors
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Cited in 174 Serials

108 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
67 Journal of Mathematical Analysis and Applications
47 Journal of Functional Analysis
39 Acta Mathematica Sinica. English Series
34 Journal of Differential Equations
34 Proceedings of the American Mathematical Society
32 Calculus of Variations and Partial Differential Equations
30 The Journal of Geometric Analysis
29 Transactions of the American Mathematical Society
28 Potential Analysis
26 Communications on Pure and Applied Analysis
22 Advances in Mathematics
22 Advanced Nonlinear Studies
18 Science China. Mathematics
17 Mathematische Annalen
16 Discrete and Continuous Dynamical Systems
15 Forum Mathematicum
13 Annali di Matematica Pura ed Applicata. Serie Quarta
13 Communications in Partial Differential Equations
12 Manuscripta Mathematica
12 The Journal of Fourier Analysis and Applications
12 Communications in Contemporary Mathematics
11 Mathematische Zeitschrift
11 Journal of Inequalities and Applications
10 Revista Matemática Iberoamericana
10 NoDEA. Nonlinear Differential Equations and Applications
10 Complex Variables and Elliptic Equations
10 Journal of Function Spaces
9 Mathematische Nachrichten
9 Abstract and Applied Analysis
9 Boundary Value Problems
8 Siberian Mathematical Journal
7 Pacific Journal of Mathematics
7 International Journal of Mathematics
7 Journal de Mathématiques Pures et Appliquées. Neuvième Série
7 Banach Journal of Mathematical Analysis
7 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
7 Advances in Nonlinear Analysis
6 Journal d’Analyse Mathématique
6 Archiv der Mathematik
6 Czechoslovak Mathematical Journal
6 Applied Mathematics Letters
6 Revista Matemática Complutense
5 Applicable Analysis
5 Journal of Mathematical Physics
5 Mathematical Methods in the Applied Sciences
5 Mathematical Notes
5 ZAMP. Zeitschrift für angewandte Mathematik und Physik
5 Annales de l’Institut Fourier
5 Electronic Journal of Differential Equations (EJDE)
5 Annales Academiae Scientiarum Fennicae. Mathematica
5 Taiwanese Journal of Mathematics
5 Mathematical Inequalities & Applications
5 Journal of Function Spaces and Applications
5 Mediterranean Journal of Mathematics
5 Journal of Pseudo-Differential Operators and Applications
4 Journal of Approximation Theory
4 Memoirs of the American Mathematical Society
4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
4 Applied Mathematics. Series B (English Edition)
4 Journal of Evolution Equations
4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
4 Frontiers of Mathematics in China
4 Journal of Mathematical Inequalities
3 Rocky Mountain Journal of Mathematics
3 Studia Mathematica
3 Integral Equations and Operator Theory
3 Monatshefte für Mathematik
3 Acta Applicandae Mathematicae
3 Annals of Global Analysis and Geometry
3 Acta Mathematicae Applicatae Sinica. English Series
3 SIAM Journal on Mathematical Analysis
3 Bulletin des Sciences Mathématiques
3 Communications in Nonlinear Science and Numerical Simulation
3 Nonlinear Analysis. Real World Applications
3 Journal of the Australian Mathematical Society
3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
3 Advances in Calculus of Variations
3 Analysis and Mathematical Physics
3 Analysis and Geometry in Metric Spaces
2 Computers & Mathematics with Applications
2 Communications on Pure and Applied Mathematics
2 Indian Journal of Pure & Applied Mathematics
2 Nonlinearity
2 Mathematics of Computation
2 Canadian Journal of Mathematics
2 Duke Mathematical Journal
2 Indiana University Mathematics Journal
2 Journal of Computational and Applied Mathematics
2 Journal of the Mathematical Society of Japan
2 Nagoya Mathematical Journal
2 Rendiconti del Seminario Matematico della Università di Padova
2 Ricerche di Matematica
2 Zeitschrift für Analysis und ihre Anwendungen
2 Chinese Annals of Mathematics. Series B
2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
2 St. Petersburg Mathematical Journal
2 Turkish Journal of Mathematics
2 Journal of Convex Analysis
...and 74 more Serials
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Cited in 41 Fields

626 Partial differential equations (35-XX)
331 Harmonic analysis on Euclidean spaces (42-XX)
278 Functional analysis (46-XX)
144 Real functions (26-XX)
100 Operator theory (47-XX)
73 Abstract harmonic analysis (43-XX)
63 Global analysis, analysis on manifolds (58-XX)
51 Calculus of variations and optimal control; optimization (49-XX)
50 Topological groups, Lie groups (22-XX)
49 Differential geometry (53-XX)
43 Integral equations (45-XX)
42 Potential theory (31-XX)
35 Functions of a complex variable (30-XX)
18 Several complex variables and analytic spaces (32-XX)
13 Convex and discrete geometry (52-XX)
10 Probability theory and stochastic processes (60-XX)
10 Numerical analysis (65-XX)
9 Measure and integration (28-XX)
9 Ordinary differential equations (34-XX)
7 Fluid mechanics (76-XX)
6 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
5 Approximations and expansions (41-XX)
4 Dynamical systems and ergodic theory (37-XX)
4 Information and communication theory, circuits (94-XX)
3 Combinatorics (05-XX)
3 Special functions (33-XX)
3 Difference and functional equations (39-XX)
3 Quantum theory (81-XX)
3 Biology and other natural sciences (92-XX)
2 Nonassociative rings and algebras (17-XX)
2 Group theory and generalizations (20-XX)
2 Manifolds and cell complexes (57-XX)
2 Computer science (68-XX)
1 Number theory (11-XX)
1 Linear and multilinear algebra; matrix theory (15-XX)
1 Integral transforms, operational calculus (44-XX)
1 General topology (54-XX)
1 Algebraic topology (55-XX)
1 Mechanics of particles and systems (70-XX)
1 Statistical mechanics, structure of matter (82-XX)
1 Systems theory; control (93-XX)

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