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## Lu, Shanzhen

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 Author ID: lu.shanzhen Published as: Lu, S.; Lu, Shan Zhen; Lu, Shan-Zhen; Lu, Shan-zhen; Lu, ShanZhen; Lu, Shanzen; Lu, Shanzhen External Links: MGP · dblp · GND
 Documents Indexed: 275 Publications since 1980, including 3 Books Biographic References: 1 Publication
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#### Co-Authors

 30 single-authored 51 Yang, Dachun 26 Ding, Yong 19 Fu, Zunwei 14 Hu, Guoen 10 Jiang, Yinsheng 10 Mo, Huixia 10 Shi, Shaoguang 9 Lin, Yan 9 Yan, Dunyan 9 Zhao, Fayou 8 Chen, Wengu 8 Li, Guoquan 8 Liu, Zongguang 6 Fan, Dashan 6 Zhang, Pu 5 Chen, Dongxiang 5 Liu, Lanzhe 5 Pan, Yibiao 5 Wu, Qiang 5 Xia, Xia 5 Xue, Qingying 5 Yabuta, Kôzô 5 Yu, Xiao 5 Zhou, Zusheng 4 Li, Junfeng 4 Liu, Heping 4 Liu, Mingju 4 Liu, Zhixin 4 Lu, Guozhen 3 Lan, Senhua 3 Li, Xiaochun 3 Soria, Fernando 3 Wu, Huoxiong 3 Xu, Lifang 3 Zheng, Xuean 2 Chen, Guoliang 2 Grafakos, Loukas 2 Gui, Yiqing 2 Han, Yongsheng 2 Lan, Jiacheng 2 Liu, Weiquan 2 Ma, Bolin 2 Meng, Yan 2 Tao, Shuangping 2 Weiss, Guido L. 2 Wu, Qingyan 2 Yuan, Wen 2 Zhang, Yan 1 Chen, Yanping 1 Cohn, William S. 1 Gong, Shuli 1 Han, Haiyan 1 Li, Dengfeng 1 Li, Wenming 1 Liu, Liguang 1 Ma, Huixia 1 Mao, Blin 1 Mao, Suzhen 1 Qiu, Qirong 1 Sato, Shûichi 1 Shao, Shuanglin 1 Si, Zengyan 1 Taibleson, Mitchell H. 1 Tan, Changmei 1 Tang, Lin 1 Tao, Guiping 1 Wang, Hongbin 1 Wang, Shiming 1 Wang, Shimo 1 Wu, Congming 1 Wu, Hoxiong 1 Xu, Zhenze
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#### Serials

 33 Journal of Beijing Normal University. Natural Science 21 Acta Mathematica Sinica. English Series 17 Science in China. Series A 16 Acta Mathematica Sinica 11 Approximation Theory and its Applications 9 Frontiers of Mathematics in China 8 Proceedings of the American Mathematical Society 7 Journal of Mathematical Analysis and Applications 7 Mathematische Nachrichten 7 Advances in Mathematics 6 Studia Mathematica 6 Hokkaido Mathematical Journal 6 Acta Mathematica Scientia. Series B. (English Edition) 5 Integral Equations and Operator Theory 5 Nagoya Mathematical Journal 5 Acta Mathematica Sinica. New Series 5 Chinese Science Bulletin 4 Tohoku Mathematical Journal. Second Series 4 Chinese Annals of Mathematics. Series A 4 Scientia Sinica. Series A 4 Kexue Tongbao 4 Acta Mathematica Scientia. Series A. (Chinese Edition) 4 Science China. Mathematics 3 Acta Mathematicae Applicatae Sinica. English Series 3 Abstract and Applied Analysis 3 Progress in Natural Science 3 Analysis in Theory and Applications 3 Acta Mathematica Sinica. Chinese Series 2 Canadian Journal of Mathematics 2 Colloquium Mathematicum 2 Kodai Mathematical Journal 2 Pacific Journal of Mathematics 2 Publicacions Matemàtiques 2 Forum Mathematicum 2 Georgian Mathematical Journal 2 International Journal of Applied Mathematical Sciences 2 Journal of Mathematical Inequalities 2 Jordan Journal of Mathematics and Statistics 1 Analysis Mathematica 1 Houston Journal of Mathematics 1 Arkiv för Matematik 1 Annales des Sciences Mathématiques du Québec 1 Collectanea Mathematica 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Functional Analysis 1 Journal of the Mathematical Society of Japan 1 Mathematische Zeitschrift 1 Michigan Mathematical Journal 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Southeast Asian Bulletin of Mathematics 1 Journal of Mathematical Research & Exposition 1 Chinese Annals of Mathematics. Series B 1 Constructive Approximation 1 Northeastern Mathematical Journal 1 Revista Matemática Iberoamericana 1 Panamerican Mathematical Journal 1 Journal of the Australian Mathematical Society. Series A 1 Journal of Partial Differential Equations 1 Turkish Journal of Mathematics 1 The Journal of Fourier Analysis and Applications 1 Communications in Applied Analysis 1 Taiwanese Journal of Mathematics 1 Journal of Inequalities and Applications 1 Mathematical Sciences Research Hot-Line 1 Mathematical Inequalities & Applications 1 Journal of the Australian Mathematical Society 1 Journal of Function Spaces and Applications 1 Scientia Sinica 1 Pure and Applied Mathematics Quarterly
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#### Fields

 253 Harmonic analysis on Euclidean spaces (42-XX) 70 Operator theory (47-XX) 41 Functional analysis (46-XX) 18 Abstract harmonic analysis (43-XX) 16 Partial differential equations (35-XX) 14 Real functions (26-XX) 5 Approximations and expansions (41-XX) 2 Number theory (11-XX) 2 Potential theory (31-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Integral equations (45-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH Open

183 Publications have been cited 1,590 times in 780 Documents Cited by Year
Four lectures on real $$H^ p$$ spaces. Zbl 0839.42005
Lu, Shanzhen
1995
Singular integrals and related topics. Zbl 1124.42011
Lu, Shanzhen; Ding, Yong; Yan, Dunyan
2007
Weighted norm inequalities for fractional integral operators with rough kernel. Zbl 0905.42010
Ding, Yong; Lu, Shanzhen
1998
The decomposition of weighted Herz space on $$\mathbb{R}^ n$$ and its applications. Zbl 0830.42014
Lu, Shanzhen; Yang, Dachun
1995
The central BMO spaces and Littlewood-Paley operators. Zbl 0857.42009
Lu, Shanzhen; Yang, Dachun
1995
The weighted Herz-type Hardy space and its applications. Zbl 0832.42013
Lu, Shanzhen; Yang, Dachun
1995
Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients. Zbl 0917.35017
Fan, Dashan; Lu, Shanzhen; Yang, Dachun
1998
Criterion on $$L^ p$$-boundedness for a class of oscillatory singular integrals with rough kernels. Zbl 0786.42007
Lu, Shanzhen; Zhang, Yan
1992
On commutators of Marcinkiewicz integrals with rough kernel. Zbl 1019.42009
Ding, Yong; Lu, Shanzhen; Yabuta, Kôzô
2002
Sharp bounds for $$m$$-linear Hardy and Hilbert operators. Zbl 1248.42020
Fu, Zunwei; Grafakos, Loukas; Lu, Shanzhen; Zhao, Fayou
2012
Characterization for commutators of $$n$$-dimensional fractional Hardy operators. Zbl 1131.42012
Fu, Zunwei; Liu, Zongguang; Lu, Shanzhen; Wang, Hongbin
2007
A problem on rough parametric Marcinkiewicz functions. Zbl 0993.42008
Ding, Yong; Lu, Shanzhen; Yabuta, Kôzô
2002
Higher order commutators for a class of rough operators. Zbl 1038.42013
Ding, Young; Lu, Shanzhen
1999
$$\lambda$$-central $$BMO$$ estimates for commutators of singular integral operators with rough kernels. Zbl 1142.42004
Fu, Zun Wei; Lin, Yan; Lu, Shan Zhen
2008
Weighted boundedness for a class of rough multilinear operators. Zbl 0985.42011
Ding, Yong; Lu, Shanzhen
2001
The local versions of $$H^p(\mathbb{R}^n)$$ spaces at the origin. Zbl 0935.42012
Lu, Shanzhen; Yang, Dachun
1995
Homogeneous fractional integrals on Hardy spaces. Zbl 0959.42011
Ding, Yong; Lu, Shanzhen
2000
The Littlewood-Paley function and $$\varphi$$-transform characterizations of a new Hardy space $$HK_ 2$$ associated with the Herz space. Zbl 0811.42005
Lu, Shanzhen; Yang, Dachun
1992
Boundedness of rough singular integral operators on the homogeneous Morrey-Herz spaces. Zbl 1081.42012
Lu, Shanzhen; Xu, Lifang
2005
The continuity of commutators on Herz-type spaces. Zbl 0913.42016
Lu, Shanzhen; Yang, Dachun
1997
Boundedness of operators in Morrey spaces on homogeneous spaces and its applications. Zbl 0916.43006
Fan, Dashan; Lu, Shanzhen; Yang, Dachun
1998
Marcinkiewicz integral on Hardy spaces. Zbl 0994.42013
Ding, Yong; Lu, Shanzhen; Xue, Qingying
2002
Boundedness of some sublinear operators in weighted Herz-type spaces. Zbl 0986.42010
Lu, Shanzhen; Yabuta, Kôzô; Yang, Dachun
2000
Hardy-Littlewood-Sobolev theorems of fractional integration on Herz-type spaces and its applications. Zbl 0893.42005
Lu, Shanzhen; Yang, Dachun
1996
Commutators of weighted Hardy operators on $$\mathbb {R}^{n}$$. Zbl 1174.42018
Fu, Zun Wei; Liu, Zong Guang; Lu, Shan Zhen
2009
Boundedness of commutators on Hardy type spaces. Zbl 1098.42009
Lu, Shanzhen; Wu, Qiang; Yang, Dachun
2002
Endpoint estimates for $$n$$-dimensional Hardy operators and their commutators. Zbl 1257.26015
Zhao, FaYou; Fu, ZunWei; Lu, ShanZhen
2012
Weak estimates for commutators of fractional integral operators. Zbl 1014.42012
Ding, Yong; Lu, Shanzhen; Zhang, Pu
2001
Oscillatory singular integrals with rough kernel. Zbl 0837.42004
Jiang, Yinsheng; Lu, Shanzhen
1995
Sublinear operators with rough kernel on generalized Morrey spaces. Zbl 0895.42005
Lu, Shanzhen; Yang, Dachun; Zhou, Zusheng
1998
Parametrized Littlewood-Paley operators on Hardy and weak Hardy spaces. Zbl 1133.42030
Ding, Yong; Lu, Shanzhen; Xue, Qingying
2007
Singular integrals and commutators on homogeneous groups. Zbl 1026.43007
Lu, Guozhen; Lu, Shanzhen; Yang, Dachun
2002
Some characterizations of weighted Herz-type Hardy spaces and their applications. Zbl 0887.42015
Lu, Shanzhen; Yang, Dachun
1997
Strongly singular Calderón-Zygmund operators and their commutators. Zbl 1279.42018
Lin, Yan; Lu, Shanzhen
2008
Weighted multilinear Hardy operators and commutators. Zbl 1331.42016
Fu, Zun Wei; Gong, Shu Li; Lu, Shan Zhen; Yuan, Wen
2015
Herz-type Sobolev and Bessel potential spaces and their applications. Zbl 0901.46027
Lu, Shanzhen; Yang, Dachun
1997
Boundedness of rough singular integral operators on homogeneous Herz spaces. Zbl 0927.42010
Hu, Guoen; Lu, Shanzhen; Yang, Dachun
1999
Commutators of $$n$$-dimensional rough Hardy operators. Zbl 1226.47050
Fu, ZunWei; Lu, ShanZhen; Zhao, FaYou
2011
Weighted weak type estimates for commutators of the Marcinkiewicz integrals. Zbl 1217.42029
Ding, Yong; Lu, Shanzhen; Zhang, Pu
2004
Rough singular integrals associated to surfaces of revolution. Zbl 0976.42009
Lu, Shanzhen; Pan, Yibiao; Yang, Dachun
2001
Weighted $$L^ p$$-boundedness for higher order commutators of oscillatory singular integrals. Zbl 0873.42009
Ding, Yong; Lu, Shanzhen
1996
Oscillatory singular integrals on Hardy spaces associated with Herz spaces. Zbl 0830.42008
Lu, Shanzhen; Yang, Dachun
1995
Sharp bounds for Hardy type operators on higher-dimensional product spaces. Zbl 1284.26022
Lu, Shanzhen; Yan, Dunyan; Zhao, Fayou
2013
On Marcinkiewicz integral with homogeneous kernels. Zbl 0961.42014
Ding, Yong; Lu, Shanzhen; Xue, Qingying
2000
The weak Herz spaces. Zbl 0887.42016
Hu, Guoen; Lu, Shanzhen; Yang, Dachun
1997
Sharp estimates of $$p$$-adic Hardy and Hardy-Littlewood-Pólya operators. Zbl 1279.42023
Fu, Zun Wei; Wu, Qing Yan; Lu, Shan Zhen
2013
Weighted Hardy operators and commutators on Morrey spaces. Zbl 1206.42027
Fu, Zunwei; Lu, Shanzhen
2010
Multilinear singular and fractional integrals. Zbl 1129.42352
Ding, Yong; Lu, Shanzhen; Yabuta, Kôzô
2006
Lipschitz estimates for generalized commutators of fractional integrals with rough kernel. Zbl 1049.42009
Lu, Shanzhen; Zhang, Pu
2003
$$L^ p$$-boundedness of multilinear oscillatory singular integrals with Calderón-Zygmund kernel. Zbl 1054.42013
Lu, Shanzhen; Yan, Dunyan
2002
Inhomogeneous Besov and Triebel-Lizorkin spaces on spaces of homgeneous type. Zbl 0957.46025
Han, Yongsheng; Lu, Shanzhen; Yang, Dachun
1999
Criterion of $$(L^p,L^r)$$ boundedness for a class of multilinear oscillatory singular integrals. Zbl 0929.42008
Chen, Wengu; Hu, Guoen; Lu, Shanzhen
1998
The commutator of the Bochner-Riesz operator. Zbl 0889.42011
Hu, Guoen; Lu, Shanzhen
1996
A class of singular integral operators with rough kernel on product domains. Zbl 0830.42006
Jiang, Yinsheng; Lu, Shanzhen
1995
The weighted norm inequality for a class of oscillatory integral operators. Zbl 0801.42009
Lu, Shanzhen; Zhang, Yan
1992
Bochner-Riesz means on Euclidean spaces. Zbl 1281.42003
Lu, Shanzhen; Yan, Dunyan
2013
The multilinear Marcinkiewicz interpolation theorem revisited: the behavior of the constant. Zbl 1242.46025
Grafakos, Loukas; Liu, Liguang; Lu, Shanzhen; Zhao, Fayou
2012
Commutators of generalized Hardy operators. Zbl 1173.42009
Fu, Zunwei; Lu, Shanzhen
2009
Parametrized area integrals on Hardy spaces and weak Hardy spaces. Zbl 1123.42003
Ding, Yong; Lu, Shan Zhen; Xue, Qing Ying
2007
CBMO estimates for commutators and multilinear singular integrals. Zbl 1081.42011
Lu, Shanzhen; Wu, Qiang
2004
Multilinear singular integrals with rough kernel. Zbl 1023.42009
Lu, Shan Zhen; Wu, Huo Xiong; Zhang, Pu
2003
Continuity of higher order commutators on certain Hardy spaces. Zbl 1024.42008
Ding, Yong; Lu, Shanzhen; Zhang, Pu
2002
Inhomogeneous discrete Calderón reproducing formulas for spaces of homogeneous type. Zbl 0991.43004
Han, Yongsheng; Lu, Shanzhen; Yang, Dachun
2001
Explicit constants for hardy’s inequality with power weight on $$n$$-dimensional product spaces. Zbl 1258.42020
Wang, ShiMo; Lu, ShanZhen; Yan, DunYan
2012
On weighted weak type norm inequalities for one-sided oscillatory singular integrals. Zbl 1257.42022
Fu, Zunwei; Lu, Shanzhen; Sato, Shuichi; Shi, Shaoguang
2011
Toeplitz operators related to strongly singular Calderón–Zygmund operators. Zbl 1118.47019
Lin, Yan; Lu, Shanzhen
2006
Integral operators with variable kernels on weak Hardy spaces. Zbl 1099.47040
Ding, Yong; Lu, Shanzhen; Shao, Shuanglin
2006
$$L^{p} (\mathbb R^{m} \times \mathbb R^{n})$$ boundedness for the Marcinkiewicz integral on product spaces. Zbl 1217.42032
Hu, Guoen; Lu, Shanzhen; Yan, Dunyan
2003
Oscillatory singular integrals and commutators with rough kernels. Zbl 1054.42012
Lu, Shanzhen; Wu, Huoxiong
2003
Weighted weak type inequalities for maximal commutators of Bochner-Riesz operator. Zbl 1034.42015
Liu, Lanzhe; Lu, Shanzhen
2003
Boundedness of homogeneous fractional integrals on $$L^p$$ for $$N/\alpha{\leq}p{\leq}{\infty}$$. Zbl 1031.42015
Ding, Yong; Lu, Shanzhen
2002
Multiplier theorems for Herz type Hardy spaces. Zbl 0905.42007
Lu, Shanzhen; Yang, Dachun
1998
The decomposition of Herz spaces on local fields and its applications. Zbl 0844.43008
Lu, Shanzhen; Yang, Dachun
1995
$$L^ p$$ boundedness of a class of maximal singular integral operators. Zbl 0759.42013
Jiang, Yinsheng; Lu, Shanzhen
1992
The best bound for $$n$$-dimensional fractional Hardy operators. Zbl 1307.26026
Zhao, Fayou; Lu, Shanzhen
2015
Weighted estimates for iterated commutators of multilinear fractional operators. Zbl 1261.42026
Si, Zeng Yan; Lu, Shan Zhen
2012
$$L^p$$ boundedness of a parabolic Littlewood-Paley operator with rough kernel belonging to $$F_\alpha (S^{n-1})$$. Zbl 1240.42097
Chen, Dongxiang; Lu, Shanzhen
2011
Toeplitz-type operators on Lebesgue spaces. Zbl 1199.42074
Lu, Shanzhen; Ma, Huixia
2009
Boundedness of commutators on Hardy-type spaces. Zbl 1134.42314
Lin, Yan; Lu, Shanzhen
2007
Hardy spaces estimates for multilinear operators with homogeneous kernels. Zbl 1036.42015
Ding, Yong; Lu, Shanzhen
2003
The $$L^{p_ 1} \times L^{p_ 2} \times \cdots \times L^{p_ k}$$ boundedness for some rough operators. Zbl 0882.42010
Ding, Yong; Lu, Shanzhen
1996
Some new Hardy spaces associated with Herz spaces and their wavelet characterizations. Zbl 0782.42019
Lu, Shanzhen; Yang, Dachun
1993
Characterization of the central Campanato space via the commutator operator of Hardy type. Zbl 1317.42022
Shi, Shaoguang; Lu, Shanzhen
2015
Conjectures and problems on Bochner-Riesz means. Zbl 1306.42010
Lu, Shanzhen
2013
Some characterizations of Campanato spaces via commutators on Morrey spaces. Zbl 1273.42015
Shi, Shaoguang; Lu, Shanzhen
2013
Pseudo-differential operators on Sobolev and Lipschitz spaces. Zbl 1185.42012
Lin, Yan; Lu, Shan Zhen
2010
Vector-valued singular integral operators with non-smooth kernels and related multilinear commutators. Zbl 1159.42012
Mo, Hui-Xia; Lu, Shan-Zhen
2007
Boundedness of multilinear singular integral operators on Hardy and Herz-type spaces. Zbl 1213.42049
Lin, Yan; Lu, Shanzhen
2007
Two-weight weak-type norm inequalities for the commutators of fractional integrals. Zbl 1072.42012
Liu, Zongguang; Lu, Shanzhen
2004
Endpoint estimates for commutators of Calderón-Zygmund type operators. Zbl 1003.42010
Liu, Zongguang; Lu, Shanzhen
2002
Multilinear oscillatory integrals with Calderón-Zygmund kernel. Zbl 0954.42008
Lu, Shanzhen
1999
Boundedness of commutators on homogeneous Herz spaces. Zbl 0929.42009
Lu, Shanzhen; Tang, Lin; Yang, Dachun
1998
The applications of weak Herz spaces. Zbl 0915.42012
Hu, Guoen; Lu, Shanzhen; Yang, Dachun
1997
Transference and restriction of maximal multiplier operators on Hardy spaces. Zbl 0812.42010
Liu, Zhixin; Lu, Shanzhen
1993
On block decomposition of functions. Zbl 0572.42012
Lu, Shanzhen
1984
Some one-sided estimates for oscillatory singular integrals. Zbl 1293.42013
Fu, Zunwei; Lu, Shanzhen; Pan, Yibiao; Shi, Shaoguang
2014
A weighted variant of Riemann-Liouville fractional integrals on $$\mathbb R^n$$. Zbl 1253.26009
Fu, Zun Wei; Lu, Shan Zhen; Yuan, Wen
2012
Weighted estimates for the multilinear singular integral operators with non-smooth kernels. Zbl 1222.42020
Hu, Guoen; Lu, Shanzhen
2011
Boundedness of multilinear commutators of generalized fractional integrals. Zbl 1206.42014
Mo, Huixia; Lu, Shanzhen
2008
Applications of some block spaces to singular integrals. Zbl 1202.42032
Lu, Shanzhen
2007
Sharp maximal estimates for multilinear commutators of multilinear strongly singular Calderón-Zygmund operators and applications. Zbl 1409.42011
Lin, Yan; Lu, Guozhen; Lu, Shanzhen
2019
Further results on almost resolvable cycle systems and the Hamilton-Waterloo problem. Zbl 1391.05212
Wang, L.; Lu, S.; Cao, Haitao
2018
Olsen-type inequalities for the generalized commutator of multilinear fractional integrals. Zbl 1424.42039
Yu, Xiao; Lu, Shanzhen
2018
Weighted multilinear Hardy operators and commutators. Zbl 1331.42016
Fu, Zun Wei; Gong, Shu Li; Lu, Shan Zhen; Yuan, Wen
2015
The best bound for $$n$$-dimensional fractional Hardy operators. Zbl 1307.26026
Zhao, Fayou; Lu, Shanzhen
2015
Characterization of the central Campanato space via the commutator operator of Hardy type. Zbl 1317.42022
Shi, Shaoguang; Lu, Shanzhen
2015
Some one-sided estimates for oscillatory singular integrals. Zbl 1293.42013
Fu, Zunwei; Lu, Shanzhen; Pan, Yibiao; Shi, Shaoguang
2014
A characterization of Campanato space via commutator of fractional integral. Zbl 1302.42032
Shi, Shaoguang; Lu, Shanzhen
2014
Boundedness of one-sided oscillatory integral operators on weighted Lebesgue spaces. Zbl 07022102
Fu, Zunwei; Lu, Shanzhen; Pan, Yibiao; Shi, Shaoguang
2014
$$M_{p}$$ weights for bilinear Hardy operators on $$\mathbb R ^{n}$$. Zbl 1305.26042
Zhao, Fayou; Fu, Zunwei; Lu, Shanzhen
2014
Commutators generated by multilinear Calderón-Zygmund type singular integral and Lipschitz functions. Zbl 1304.42043
Mo, Hui-Xia; Lu, Shan-Zhen
2014
Sharp bounds for Hardy type operators on higher-dimensional product spaces. Zbl 1284.26022
Lu, Shanzhen; Yan, Dunyan; Zhao, Fayou
2013
Sharp estimates of $$p$$-adic Hardy and Hardy-Littlewood-Pólya operators. Zbl 1279.42023
Fu, Zun Wei; Wu, Qing Yan; Lu, Shan Zhen
2013
Bochner-Riesz means on Euclidean spaces. Zbl 1281.42003
Lu, Shanzhen; Yan, Dunyan
2013
Conjectures and problems on Bochner-Riesz means. Zbl 1306.42010
Lu, Shanzhen
2013
Some characterizations of Campanato spaces via commutators on Morrey spaces. Zbl 1273.42015
Shi, Shaoguang; Lu, Shanzhen
2013
Endpoint estimates for generalized commutators of Hardy operators on $$H^1$$ space. Zbl 1383.42016
Yu, Xiao; Lu, Shanzhen
2013
A characterization of $$\lambda$$-central BMO space. Zbl 1260.47035
Zhao, Fayou; Lu, Shanzhen
2013
Some recent progress of $$n$$-dimensional Hardy operators. Zbl 1313.42001
Lu, Shanzhen
2013
Sharp bounds for $$m$$-linear Hardy and Hilbert operators. Zbl 1248.42020
Fu, Zunwei; Grafakos, Loukas; Lu, Shanzhen; Zhao, Fayou
2012
Endpoint estimates for $$n$$-dimensional Hardy operators and their commutators. Zbl 1257.26015
Zhao, FaYou; Fu, ZunWei; Lu, ShanZhen
2012
The multilinear Marcinkiewicz interpolation theorem revisited: the behavior of the constant. Zbl 1242.46025
Grafakos, Loukas; Liu, Liguang; Lu, Shanzhen; Zhao, Fayou
2012
Explicit constants for hardy’s inequality with power weight on $$n$$-dimensional product spaces. Zbl 1258.42020
Wang, ShiMo; Lu, ShanZhen; Yan, DunYan
2012
Weighted estimates for iterated commutators of multilinear fractional operators. Zbl 1261.42026
Si, Zeng Yan; Lu, Shan Zhen
2012
A weighted variant of Riemann-Liouville fractional integrals on $$\mathbb R^n$$. Zbl 1253.26009
Fu, Zun Wei; Lu, Shan Zhen; Yuan, Wen
2012
Commutators of $$n$$-dimensional rough Hardy operators. Zbl 1226.47050
Fu, ZunWei; Lu, ShanZhen; Zhao, FaYou
2011
On weighted weak type norm inequalities for one-sided oscillatory singular integrals. Zbl 1257.42022
Fu, Zunwei; Lu, Shanzhen; Sato, Shuichi; Shi, Shaoguang
2011
$$L^p$$ boundedness of a parabolic Littlewood-Paley operator with rough kernel belonging to $$F_\alpha (S^{n-1})$$. Zbl 1240.42097
Chen, Dongxiang; Lu, Shanzhen
2011
Weighted estimates for the multilinear singular integral operators with non-smooth kernels. Zbl 1222.42020
Hu, Guoen; Lu, Shanzhen
2011
Weighted estimates for commutators of one-sided oscillatory integral operators. Zbl 1284.42041
Shi, Shaoguang; Fu, Zunwei; Lu, Shanzhen
2011
Commutators of Bochner-Riesz operators for a class of radial functions. Zbl 1240.42033
Xia, Xia; Lu, Shanzhen
2011
Some results and problems on commutators. Zbl 1227.42016
Lu, Shanzhen
2011
$$L^{p}$$ boundedness for commutators of parabolic Littlewood-Paley operators with rough kernels. Zbl 1245.42018
Chen, Dongxiang; Lu, Shanzhen
2011
Weighted Hardy operators and commutators on Morrey spaces. Zbl 1206.42027
Fu, Zunwei; Lu, Shanzhen
2010
Pseudo-differential operators on Sobolev and Lipschitz spaces. Zbl 1185.42012
Lin, Yan; Lu, Shan Zhen
2010
CBMO estimates for multilinear Hardy operators. Zbl 1202.42031
Lu, Shan Zhen; Zhao, Fa You
2010
Commutators of weighted Hardy operators on $$\mathbb {R}^{n}$$. Zbl 1174.42018
Fu, Zun Wei; Liu, Zong Guang; Lu, Shan Zhen
2009
Commutators of generalized Hardy operators. Zbl 1173.42009
Fu, Zunwei; Lu, Shanzhen
2009
Toeplitz-type operators on Lebesgue spaces. Zbl 1199.42074
Lu, Shanzhen; Ma, Huixia
2009
$$\lambda$$-central $$BMO$$ estimates for commutators of singular integral operators with rough kernels. Zbl 1142.42004
Fu, Zun Wei; Lin, Yan; Lu, Shan Zhen
2008
Strongly singular Calderón-Zygmund operators and their commutators. Zbl 1279.42018
Lin, Yan; Lu, Shanzhen
2008
Boundedness of multilinear commutators of generalized fractional integrals. Zbl 1206.42014
Mo, Huixia; Lu, Shanzhen
2008
Multipliers and Herz type spaces. Zbl 1176.42009
Lu, ShanZhen
2008
New Hardy spaces associated with some anisotropic Herz spaces and their applications. Zbl 1176.42018
Ding, Yong; Lan, Senhua; Lu, Shanzhen
2008
Boundedness of multilinear operators related to fractional integral with rough kernel on Hardy spaces. Zbl 1174.42319
Han, Haiyan; Lu, Shanzhen
2008
Boundedness of commutators of an oscillatory integral operator. Zbl 1213.42054
Xia, Xia; Lu, Shanzhen
2008
Singular integrals and related topics. Zbl 1124.42011
Lu, Shanzhen; Ding, Yong; Yan, Dunyan
2007
Characterization for commutators of $$n$$-dimensional fractional Hardy operators. Zbl 1131.42012
Fu, Zunwei; Liu, Zongguang; Lu, Shanzhen; Wang, Hongbin
2007
Parametrized Littlewood-Paley operators on Hardy and weak Hardy spaces. Zbl 1133.42030
Ding, Yong; Lu, Shanzhen; Xue, Qingying
2007
Parametrized area integrals on Hardy spaces and weak Hardy spaces. Zbl 1123.42003
Ding, Yong; Lu, Shan Zhen; Xue, Qing Ying
2007
Boundedness of commutators on Hardy-type spaces. Zbl 1134.42314
Lin, Yan; Lu, Shanzhen
2007
Vector-valued singular integral operators with non-smooth kernels and related multilinear commutators. Zbl 1159.42012
Mo, Hui-Xia; Lu, Shan-Zhen
2007
Boundedness of multilinear singular integral operators on Hardy and Herz-type spaces. Zbl 1213.42049
Lin, Yan; Lu, Shanzhen
2007
Applications of some block spaces to singular integrals. Zbl 1202.42032
Lu, Shanzhen
2007
Boundedness of generalized higher commutators of Marcinkiewicz integrals. Zbl 1150.42010
Mo, Huixia; Lu, Shanzhen
2007
Global regularity in homogeneous Morrey-Herz spaces of solutions to nondivergence elliptic equations with VMO coefficients. Zbl 1142.35383
Lu, Shanzhen; Tao, Shuangping
2007
A note on commutators of Bochner-Riesz operator. Zbl 1260.42007
Lu, Shanzhen; Xia, Xia
2007
Boundedness for commutators of Bochner-Riesz operators below a critical index. Zbl 1134.42003
Lu, Shan-zhen; Xia, Xia
2007
Remarks on $$g$$-functions on $$\mathbb H^n$$. Zbl 1113.42016
Liu, Mingju; Lu, Shanzhen
2007
The boundedness for commutators of multipliers. Zbl 1118.42004
Li, Wen-Ming; Lu, Shan-Zhen; Mo, Hui-Xia
2007
Multilinear singular and fractional integrals. Zbl 1129.42352
Ding, Yong; Lu, Shanzhen; Yabuta, Kôzô
2006
Toeplitz operators related to strongly singular Calderón–Zygmund operators. Zbl 1118.47019
Lin, Yan; Lu, Shanzhen
2006
Integral operators with variable kernels on weak Hardy spaces. Zbl 1099.47040
Ding, Yong; Lu, Shanzhen; Shao, Shuanglin
2006
The boundedness of commutators for the Marcinkiewicz integrals. Zbl 1187.42019
Lu, Shanzhen; Mo, Huixia
2006
Boundedness of higher-order Marcinkiewicz-type integrals. Zbl 1123.45008
Lu, Shanzhen; Mo, Huixia
2006
Multilinear Calderón-Zygmund operator on Morrey type spaces. Zbl 1213.42048
Lin, Yan; Lu, Shanzen
2006
Boundedness of some Marcinkiewicz integral operators related to higher order commutators on Hardy spaces. Zbl 1129.42368
Lu, Shanzhen; Xu, Lifang
2006
Continuity for maximal multilinear Bochner-Riesz operators on Hardy and Herz-Hardy spaces. Zbl 1129.42366
Liu, Lanzhe; Lu, Shanzhen
2006
Strongly singular integral operators on weighted Hardy space. Zbl 1129.42382
Li, Junfeng; Lu, Shanzhen
2006
$$L^{p}$$ estimates for multilinear operators of strongly singular integral operators. Zbl 1100.42011
Li, Junfeng; Lu, Shanzhen
2006
Boundedness of rough singular integral operators on the homogeneous Morrey-Herz spaces. Zbl 1081.42012
Lu, Shanzhen; Xu, Lifang
2005
A class of oscillatory singular integrals. Zbl 1078.42006
Lu, Shanzhen
2005
Boundedness of some fractional integral operators on weighted Herz type Hardy spaces. Zbl 1074.42007
Lan, Jiacheng; Lu, Shanzhen
2005
The boundedness of multilinear operators of strongly singular integral operators on Hardy spaces. Zbl 1089.42007
Li, Junfeng; Lu, Shanzhen
2005
Weighted weak type estimates for commutators of the Marcinkiewicz integrals. Zbl 1217.42029
Ding, Yong; Lu, Shanzhen; Zhang, Pu
2004
CBMO estimates for commutators and multilinear singular integrals. Zbl 1081.42011
Lu, Shanzhen; Wu, Qiang
2004
Two-weight weak-type norm inequalities for the commutators of fractional integrals. Zbl 1072.42012
Liu, Zongguang; Lu, Shanzhen
2004
On the commutators of singular integrals related to block spaces. Zbl 1057.42015
Lu, Shanzhen; Wu, Hoxiong
2004
Applications of the scale changing method to boundedness of certain commutators. Zbl 1083.42013
Li, Junfeng; Lu, Shanzhen
2004
A class of multilinear oscillatory singular integrals related to block spaces. Zbl 1059.42012
Lu, Shanzhen; Wu, Huoxiong
2004
Boundedness of commutators related to Marcinkiewicz integrals on Hardy type spaces. Zbl 1078.42007
Lu, Shanzhen; Xu, Lifang
2004
Weighted Lipschitz estimates for the multilinear fractional integrals. Zbl 1079.42005
Lan, Jiacheng; Lu, Shanzhen
2004
Boundedness criterion for multilinear oscillatory integrals with rough kernels. Zbl 1078.42004
Chen, Wengu; Lu, Shanzhen
2004
Lipschitz estimates for generalized commutators of fractional integrals with rough kernel. Zbl 1049.42009
Lu, Shanzhen; Zhang, Pu
2003
Multilinear singular integrals with rough kernel. Zbl 1023.42009
Lu, Shan Zhen; Wu, Huo Xiong; Zhang, Pu
2003
$$L^{p} (\mathbb R^{m} \times \mathbb R^{n})$$ boundedness for the Marcinkiewicz integral on product spaces. Zbl 1217.42032
Hu, Guoen; Lu, Shanzhen; Yan, Dunyan
2003
Oscillatory singular integrals and commutators with rough kernels. Zbl 1054.42012
Lu, Shanzhen; Wu, Huoxiong
2003
Weighted weak type inequalities for maximal commutators of Bochner-Riesz operator. Zbl 1034.42015
Liu, Lanzhe; Lu, Shanzhen
2003
Hardy spaces estimates for multilinear operators with homogeneous kernels. Zbl 1036.42015
Ding, Yong; Lu, Shanzhen
2003
Continuity properties for the maximal operator associated with the commutator of the Bochner-Riesz operator. Zbl 1038.42014
Liu, Zongguang; Lu, Guozhen; Lu, Shanzhen
2003
Higher order Poincaré inequalities associated with linear operators on stratified groups and applications. Zbl 1023.46032
Cohn, William S.; Lu, Guozhen; Lu, Shanzhen
2003
Endpoint estimates for certain commutators of fractional and singular integrals. Zbl 1018.42010
Lu, Shanzhen; Wu, Qiang
2003
On commutators of Marcinkiewicz integrals with rough kernel. Zbl 1019.42009
Ding, Yong; Lu, Shanzhen; Yabuta, Kôzô
2002
A problem on rough parametric Marcinkiewicz functions. Zbl 0993.42008
Ding, Yong; Lu, Shanzhen; Yabuta, Kôzô
2002
Marcinkiewicz integral on Hardy spaces. Zbl 0994.42013
Ding, Yong; Lu, Shanzhen; Xue, Qingying
2002
Boundedness of commutators on Hardy type spaces. Zbl 1098.42009
Lu, Shanzhen; Wu, Qiang; Yang, Dachun
2002
Singular integrals and commutators on homogeneous groups. Zbl 1026.43007
Lu, Guozhen; Lu, Shanzhen; Yang, Dachun
2002
$$L^ p$$-boundedness of multilinear oscillatory singular integrals with Calderón-Zygmund kernel. Zbl 1054.42013
Lu, Shanzhen; Yan, Dunyan
2002
Continuity of higher order commutators on certain Hardy spaces. Zbl 1024.42008
Ding, Yong; Lu, Shanzhen; Zhang, Pu
2002
Boundedness of homogeneous fractional integrals on $$L^p$$ for $$N/\alpha{\leq}p{\leq}{\infty}$$. Zbl 1031.42015
Ding, Yong; Lu, Shanzhen
2002
...and 83 more Documents
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#### Cited by 598 Authors

 69 Lu, Shanzhen 48 Yang, Dachun 39 Ding, Yong 29 Fan, Dashan 27 Fu, Zunwei 27 Wu, Huoxiong 26 Guliyev, Vagif Sabir 23 Chen, Jiecheng 21 Xue, Qingying 20 Yan, Dunyan 18 Lin, Yan 17 Chen, Yanping 17 Liu, Lanzhe 16 Wang, Hua 15 Wang, Hongbin 15 Yu, Xiao 15 Zhang, Pu 14 Xu, Jingshi 14 Zhao, Fayou 13 Shi, Shaoguang 13 Yuan, Wen 12 Ho, Kwok-Pun 12 Nguyen Minh Chuong 12 Tao, Xiangxing 12 Yabuta, Kôzô 11 Liu, Feng 11 Tang, Lin 10 Jiang, Yinsheng 10 Liu, Zongguang 10 Sawano, Yoshihiro 10 Wu, Qingyan 9 Duong, Dao Van 9 Omarova, Mehriban N. 9 Pan, Yibiao 9 Tao, Shuangping 8 Al-Salman, Ahmad 8 Gao, Guilian 8 Gurbuz, Ferit 8 Shu, Lisheng 8 Wang, Liwei 8 Wang, Yueshan 8 Weisz, Ferenc 8 Zhou, Jiang 7 Akbulut, Ali 7 Hu, Yue 7 Hussain, Amjad 7 Iida, Takeshi 7 Izuki, Mitsuo 7 Lan, Jiacheng 7 Ma, Bolin 7 Pradolini, Gladis G. 7 Si, Zengyan 6 Chen, Dongxiang 6 Hu, Guoen 6 Liu, Liguang 6 Lu, Guanghui 6 Ragusa, Maria Alessandra 6 Wang, Songbai 5 Cheng, Leslie C. 5 Lee, Ming-Yi 5 Li, Baode 5 Li, Junfeng 5 Qu, Meng 5 Samko, Natasha 5 Wei, Mingquan 5 Zhang, Chunjie 5 Zhang, Yandan 5 Zhou, Xiaosha 4 Al-Qassem, Hussain Mohammad 4 Cao, Jun 4 Drihem, Douadi 4 Dung, Kieu Huu 4 He, Qianjun 4 He, Sha 4 Lan, Senhua 4 Lin, Chincheng 4 Liu, Honghai 4 Liu, Yu 4 Lu, Guozhen 4 Matsuoka, Katsuo 4 Mo, Huixia 4 Ruan, Jianmiao 4 Serbetci, Ayhan 4 Shi, Yanlong 4 Sun, Jie 4 Sun, Lijing 4 Wen, Yongming 4 Wu, Di 4 Wu, Xiaomei 4 Yang, Sibei 4 Zhang, Yangyang 4 Zhu, Xiangrong 3 Ahmadli, Aysel A. 3 Almeida, Alexandre 3 Cao, Yonghui 3 Chen, Lungkee 3 Dong, Jianfeng 3 Feuto, Justin 3 Grafakos, Loukas 3 Guliyev, Ramin V. ...and 498 more Authors
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#### Cited in 155 Serials

 77 Acta Mathematica Sinica. English Series 57 Journal of Inequalities and Applications 48 Journal of Mathematical Analysis and Applications 44 Journal of Function Spaces 30 Analysis in Theory and Applications 28 Applied Mathematics. Series B (English Edition) 26 Frontiers of Mathematics in China 22 Science China. Mathematics 16 Mathematische Nachrichten 16 Science in China. Series A 16 Journal of Function Spaces and Applications 14 Abstract and Applied Analysis 14 Journal of Mathematical Inequalities 12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 11 The Journal of Fourier Analysis and Applications 9 Integral Equations and Operator Theory 9 Proceedings of the American Mathematical Society 8 Forum Mathematicum 8 Potential Analysis 7 Journal of Functional Analysis 7 Tohoku Mathematical Journal. Second Series 7 Transactions of the American Mathematical Society 7 Integral Transforms and Special Functions 7 Mathematical Inequalities & Applications 7 Journal of Pseudo-Differential Operators and Applications 6 Analysis Mathematica 6 Czechoslovak Mathematical Journal 6 Bulletin of the Korean Mathematical Society 6 The Journal of Geometric Analysis 6 Journal of the Australian Mathematical Society 6 Mediterranean Journal of Mathematics 6 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 6 Analysis and Mathematical Physics 6 Open Mathematics 5 Mathematical Notes 5 Rocky Mountain Journal of Mathematics 5 Rendiconti del Circolo Matemàtico di Palermo. Serie II 5 Acta Mathematicae Applicatae Sinica. English Series 5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 Revista Matemática Complutense 5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 5 Banach Journal of Mathematical Analysis 5 Journal of Nonlinear Science and Applications 5 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 4 Chinese Annals of Mathematics. Series B 4 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 4 Georgian Mathematical Journal 4 Annales Academiae Scientiarum Fennicae. Mathematica 4 Advances in Operator Theory 3 Ukrainian Mathematical Journal 3 Collectanea Mathematica 3 International Journal of Mathematics and Mathematical Sciences 3 Mathematische Zeitschrift 3 Nagoya Mathematical Journal 3 Taiwanese Journal of Mathematics 3 Complex Variables and Elliptic Equations 3 Tbilisi Mathematical Journal 3 Kyoto Journal of Mathematics 3 Annals of Functional Analysis 2 Computers & Mathematics with Applications 2 Discrete Mathematics 2 Israel Journal of Mathematics 2 Journal d’Analyse Mathématique 2 Advances in Mathematics 2 Journal of Approximation Theory 2 Journal of Computational and Applied Mathematics 2 Journal of the Korean Mathematical Society 2 Monatshefte für Mathematik 2 Tokyo Journal of Mathematics 2 Zeitschrift für Analysis und ihre Anwendungen 2 Constructive Approximation 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Acta Mathematica Sinica. New Series 2 Russian Mathematics 2 Lobachevskii Journal of Mathematics 2 Acta Mathematica Scientia. Series B. (English Edition) 2 Analysis and Applications (Singapore) 2 Complex Analysis and Operator Theory 2 Eurasian Mathematical Journal 2 Journal of Applied Analysis and Computation 1 Communications in Mathematical Physics 1 Indian Journal of Pure & Applied Mathematics 1 Letters in Mathematical Physics 1 Linear and Multilinear Algebra 1 Mathematical Methods in the Applied Sciences 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Studia Mathematica 1 Arkiv för Matematik 1 Archiv der Mathematik 1 Canadian Mathematical Bulletin 1 Demonstratio Mathematica 1 Functiones et Approximatio. Commentarii Mathematici 1 Glasgow Mathematical Journal 1 Illinois Journal of Mathematics 1 Journal of Differential Equations 1 Journal of the Mathematical Society of Japan 1 Kodai Mathematical Journal 1 Kyungpook Mathematical Journal 1 Mathematica Scandinavica ...and 55 more Serials
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#### Cited in 28 Fields

 698 Harmonic analysis on Euclidean spaces (42-XX) 179 Functional analysis (46-XX) 166 Operator theory (47-XX) 65 Partial differential equations (35-XX) 64 Real functions (26-XX) 29 Abstract harmonic analysis (43-XX) 15 Functions of a complex variable (30-XX) 13 Topological groups, Lie groups (22-XX) 12 Approximations and expansions (41-XX) 9 Potential theory (31-XX) 7 Integral transforms, operational calculus (44-XX) 5 Integral equations (45-XX) 3 Combinatorics (05-XX) 3 Numerical analysis (65-XX) 2 Number theory (11-XX) 2 Special functions (33-XX) 2 Probability theory and stochastic processes (60-XX) 2 Fluid mechanics (76-XX) 2 Quantum theory (81-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Information and communication theory, circuits (94-XX)