# zbMATH — the first resource for mathematics

## Mizuta, Yoshihiro

Compute Distance To:
 Author ID: mizuta.yoshihiro Published as: Mizuta, Yoshihiro; Mizuta, Y. Homepage: http://www.mis.hiroshima-u.ac.jp/~mizuta/ External Links: Math-Net.Ru · ORCID · dblp
 Documents Indexed: 189 Publications since 1974, including 2 Books
all top 5

#### Co-Authors

 58 single-authored 85 Shimomura, Tetsu 52 Ohno, Takao 27 Futamura, Toshihide 15 Maeda, Fumiyuki 10 Nakai, Eiichi 4 Aikawa, Hiroaki 4 Kishi, Kyoko 4 Kitaura, Keiji 3 Hästö, Peter A. 3 Nekvinda, Aleš 3 Yamauchi, Yusuke 2 Harjulehto, Petteri 2 Kenmochi, Nobuyuki 2 Kurokawa, Takahide 2 Sawano, Yoshihiro 1 Bui Huy Qui 1 Ihn, Chae Gyu 1 Kayupov, M. A. 1 Kiso, Toshihiro 1 Kumagai, Takashi 1 Matsumoto, Shigeki 1 Matsuoka, Katsuo 1 Nagai, Toshitaka 1 Qui, Bui Huy 1 Shioji, Naoki 1 Sobukawa, Takuya 1 Suzuki, Noriaki
all top 5

#### Serials

 44 Hiroshima Mathematical Journal 14 Journal of the Mathematical Society of Japan 13 Annales Academiae Scientiarum Fennicae. Mathematica 9 Journal of Mathematical Analysis and Applications 7 Mathematische Nachrichten 6 Potential Analysis 6 Mathematical Inequalities & Applications 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 RIMS Kokyuroku 5 Complex Variables and Elliptic Equations 4 Hokkaido Mathematical Journal 4 Proceedings of the American Mathematical Society 3 Illinois Journal of Mathematics 3 Nagoya Mathematical Journal 3 Osaka Journal of Mathematics 3 Analysis 2 Annales de l’Institut Fourier 2 Collectanea Mathematica 2 Czechoslovak Mathematical Journal 2 Journal of the London Mathematical Society. Second Series 2 Manuscripta Mathematica 2 Proceedings of the Japan Academy. Series A 2 Tohoku Mathematical Journal. Second Series 2 Zeitschrift für Analysis und ihre Anwendungen 2 Complex Variables. Theory and Application 2 Advances in Mathematical Sciences and Applications 2 Bulletin des Sciences Mathématiques 2 Revista Matemática Complutense 2 RIMS Kôkyûroku Bessatsu 1 Revue Roumaine de Mathématiques Pures et Appliquées 1 Studia Mathematica 1 Annales Academiae Scientiarum Fennicae. Series A I. Mathematica 1 Archiv der Mathematik 1 Glasgow Mathematical Journal 1 Kodai Mathematical Journal 1 Mathematica Scandinavica 1 Pacific Journal of Mathematics 1 Studia Scientiarum Mathematicarum Hungarica 1 Acta Mathematica Hungarica 1 Questions and Answers in General Topology 1 Forum Mathematicum 1 Communications in Numerical Methods in Engineering 1 Filomat 1 Analysis (München) 1 Far East Journal of Mathematical Sciences 1 Advanced Studies in Pure Mathematics 1 GAKUTO International Series. Mathematical Sciences and Applications
all top 5

#### Fields

 150 Potential theory (31-XX) 90 Functional analysis (46-XX) 23 Harmonic analysis on Euclidean spaces (42-XX) 11 Partial differential equations (35-XX) 9 Operator theory (47-XX) 8 Real functions (26-XX) 4 General and overarching topics; collections (00-XX) 4 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Fluid mechanics (76-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX)

#### Citations contained in zbMATH Open

130 Publications have been cited 829 times in 307 Documents Cited by Year
Boundedness of maximal operators and Sobolev’s inequality on Musielak-Orlicz-Morrey spaces. Zbl 1267.46045
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2013
Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent. Zbl 1161.46305
Mizuta, Yoshihiro; Shimomura, Tetsu
2008
Sobolev embeddings for variable exponent Riesz potentials on metric spaces. Zbl 1100.31002
Futamura, Toshihide; Mizuta, Yoshihiro; Shimomura, Tetsu
2006
Sobolev’s inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space $$L^{p(\cdot)}(\log L)^{q(\cdot)}$$. Zbl 1153.31002
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2008
Potential theory in Euclidean spaces. Zbl 0849.31001
Mizuta, Yoshihiro
1995
Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials. Zbl 1200.26007
Mizuta, Yoshihiro; Nakai, Eiichi; Ohno, Takao; Shimomura, Tetsu
2010
Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents. Zbl 1228.31004
Mizuta, Yoshihiro; Nakai, Eiichi; Ohno, Takao; Shimomura, Tetsu
2011
Continuity properties of potentials and Beppo-Levi-Deny functions. Zbl 0782.31004
Mizuta, Yoshihiro
1993
Approximate identities and Young type inequalities in Musielak-Orlicz spaces. Zbl 1313.46041
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2013
Continuity properties of Riesz potentials for function in $$L^{p(.)}$$ of variable exponent. Zbl 1087.31004
Futamura, Toshihide; Mizuta, Yoshihiro
2005
Continuity properties of Riesz potentials of Orlicz functions. Zbl 1181.46026
Mizuta, Yoshihiro; Shimomura, Tetsu
2009
Compact embeddings for Sobolev spaces of variable exponents and existence of solutions for nonlinear elliptic problems involving the $$p(x)$$-Laplacian and its critical exponent. Zbl 1202.46034
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu; Shioji, Naoki
2010
Differentiability and Hölder continuity of Riesz potentials of Orlicz functions. Zbl 0955.31002
Mizuta, Yoshihiro; Shimomura, Tetsu
2000
Sobolev embeddings for Riesz potential space of variable exponent. Zbl 1109.31004
Futamura, Toshihide; Mizuta, Yoshihiro; Shimomura, Tetsu
2006
Maximal functions, Riesz potentials and Sobolev embeddings on Musielak-Orlicz-Morrey spaces of variable exponent in $$\mathbb{R}^n$$. Zbl 1273.31005
Mizuta, Yoshihiro; Nakai, Eiichi; Ohno, Takao; Shimomura, Tetsu
2012
Continuity properties for Riesz potentials of functions in Morrey spaces of variable exponent. Zbl 1184.31005
Mizuta, Yoshihiro; Shimomura, Tetsu
2010
Approximate identities and Young type inequalities in variable Lebesgue-Orlicz spaces $$L^{p(\cdot)}(\log L)^{q(\cdot)}$$. Zbl 1216.46025
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao
2010
Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent. Zbl 1193.46016
Futamura, Toshihide; Mizuta, Yoshihiro; Shimomura, Tetsu
2010
Sobolev’s theorem and duality for Herz-Morrey spaces of variable exponent. Zbl 1288.31010
Mizuta, Yoshihiro; Ohno, Takao
2014
Sobolev’s inequality for Riesz potentials of functions in non-doubling Morrey spaces. Zbl 1186.31003
Mizuta, Yoshihiro; Shimomura, Tetsu; Sobukawa, Takuya
2009
Sobolev inequalities for Orlicz spaces of two variable exponents. Zbl 1206.46035
Hästö, Peter; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2010
Sobolev’s inequality for double phase functionals with variable exponents. Zbl 1423.46049
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2019
An elementary proof of Sobolev embeddings for Riesz potentials of functions in Morrey spaces $$L^{1,\nu,\beta}(G)$$. Zbl 1175.31005
Mizuta, Yoshihiro; Nakai, Eiichi; Ohno, Takao; Shimomura, Tetsu
2008
Tangential limits of monotone Sobolev functions. Zbl 0852.31008
Mizuta, Yoshihiro
1995
Integral representations, differentiability properties and limits at infinity for Beppo Levi functions. Zbl 0885.31004
Mizuta, Yoshihiro
1997
Crack edge element of three-dimensional displacement discontinuity method with boundary division into triangular leaf elements. Zbl 1052.74586
Li, H.; Liu, C. L.; Mizuta, Y.; Kayupov, M. A.
2001
On the boundary limits of harmonic functions with gradient in $$L^p$$. Zbl 0522.31009
Mizuta, Yoshihiro
1984
Continuity of Sobolev functions of variable exponent on metric spaces. Zbl 1072.46506
Mizuta, Yoshihiro; Shimomura, Tetsu
2004
Exponential integrability for Riesz potentials of functions in Orlicz classes. Zbl 0917.31004
Mizuta, Yoshihiro; Shimomura, Tetsu
1998
Boundary limits of spherical means for BLD and monotone BLD functions in the unit ball. Zbl 0926.31003
Mizuta, Yoshihiro; Shimomura, Tetsu
1999
Maximal functions for Lebesgue spaces with variable exponent approaching 1. Zbl 1111.46019
Futamura, Toshihide; Mizuta, Yoshihiro
2006
Sobolev embeddings for Riesz potential spaces of variable exponents near 1 and Sobolev’s exponent. Zbl 1192.46027
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2010
Taylor expansion of Riesz potentials. Zbl 0863.31005
Shimomura, Tetsu; Mizuta, Yoshihiro
1995
Integrability of maximal functions for generalized Lebesgue spaces with variable exponent. Zbl 1143.46010
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2008
A generalization of Bôcher’s theorem for polyharmonic functions. Zbl 1013.31005
Futamura, Toshihide; Kishi, Kyoko; Mizuta, Yoshihiro
2001
Continuity properties of Riesz potentials and boundary limits of Beppo Levi functions. Zbl 0698.31004
Mizuta, Yoshihiro
1988
Herz-Morrey spaces of variable exponent, Riesz potential operator and duality. Zbl 1312.31013
Mizuta, Yoshihiro; Ohno, Takao
2015
Sobolev’s inequality for Riesz potentials with variable exponent satisfying a log-Hölder condition at infinity. Zbl 1085.31005
Mizuta, Yoshihiro; Shimomura, Tetsu
2005
Existence of various boundary limits of Beppo Levi functions of higher order. Zbl 0475.31004
Mizuta, Yoshihiro
1979
Trudinger’s inequality and continuity of potentials on Musielak-Orlicz-Morrey spaces. Zbl 1268.46024
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2013
Growth properties of Musielak-Orlicz integral means for Riesz potentials. Zbl 1333.46030
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Shimomura, Tetsu
2015
Weighted Morrey spaces of variable exponent and Riesz potentials. Zbl 1318.31009
Mizuta, Yoshihiro; Shimomura, Tetsu
2015
Sobolev and Trudinger type inequalities on grand Musielak-Orlicz-Morrey spaces. Zbl 1327.31017
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2015
Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials. Zbl 1269.31005
Mizuta, Yoshihiro; Nakai, Eiichi; Sawano, Yoshihiro; Shimomura, Tetsu
2013
Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces. Zbl 1246.46034
Mizuta, Yoshihiro; Nakai, Eiichi; Sawano, Yoshihiro; Shimomura, Tetsu
2012
Isolated singularities of super-polyharmonic functions. Zbl 1073.31005
Futamura, Toshihide; Mizuta, Yoshihiro
2004
Boundary behavior of monotone Sobolev functions on John domains in a metric space. Zbl 1074.31005
Futamura, Toshihide; Mizuta, Yoshihiro
2005
Sobolev inequalities for Musielak-Orlicz spaces. Zbl 1392.46037
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2018
Vanishing exponential integrability for Riesz potentials of functions in Orlicz classes. Zbl 1152.31003
Mizuta, Yoshihiro; Shimomura, Tetsu
2007
Growth properties for modified Poisson integrals in a half space. Zbl 1056.31004
Mizuta, Yoshihiro; Shimomura, Tetsu
2004
Weighted Sobolev inequality in Musielak-Orlicz space. Zbl 1243.46020
Mizuta, Yoshihiro; Shimomura, Tetsu
2012
Boundedness of maximal operators and Sobolev’s theorem for non-homogeneous central Morrey spaces of variable exponent. Zbl 1334.31004
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2015
Boundedness of the maximal operator and Sobolev’s inequality on non-homogeneous central Herz-Morrey-Orlicz spaces. Zbl 1325.31002
Mizuta, Yoshihiro; Ohno, Takao
2015
Trudinger’s exponential integrability for Riesz potentials of functions in generalized grand Morrey spaces. Zbl 1305.42017
Mizuta, Yoshihiro; Ohno, Takao
2014
Sobolev’s inequality for Riesz potentials of functions in Morrey spaces of integral form. Zbl 1211.46026
Mizuta, Yoshihiro; Shimomura, Tetsu
2010
Variable exponent weighted norm inequality for generalized Riesz potentials on the unit ball. Zbl 1405.46023
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Shimomura, Tetsu
2018
Continuity and differentiability for weighted Sobolev spaces. Zbl 1029.46032
Mizuta, Yoshihiro; Shimomura, Tetsu
2002
Integral representations of Beppo Levi functions of higher order. Zbl 0287.31005
Mizuta, Yoshihiro
1974
Removability of sets for sub-polyharmonic functions. Zbl 1041.31004
Futamura, Toshihide; Kishi, Kyoko; Mizuta, Yoshihiro
2003
Maximal functions, Riesz potentials and Sobolev’s inequality in generalized Lebesgue spaces. Zbl 1125.31001
Mizuta, Yoshihiro; Shimomura, Tetsu
2006
Growth properties of potentials in central Morrey-Orlicz spaces on the unit ball. Zbl 1396.31004
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2018
Optimal estimates for the fractional Hardy operator. Zbl 1328.47049
Mizuta, Yoshihiro; Nekvinda, Aleš; Shimomura, Tetsu
2015
Sobolev’s theorem for Riesz potentials of functions in grand Morrey spaces of variable exponent. Zbl 1332.31007
Futamura, Toshihide; Mizuta, Yoshihiro; Ohno, Takao
2014
Duality of non-homogeneous central Herz-Morrey-Musielak-Orlicz spaces. Dedicated to Professor Hiroaki Aikawa on the occasion of his sixtieth birthday. Zbl 1387.46029
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2017
Sobolev’s theorem for double phase functionals. Zbl 1453.46021
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2020
Hardy averaging operator on generalized Banach function spaces and duality. Zbl 1286.47030
Mizuta, Yoshihiro; Nekvinda, Aleš; Shimomura, Tetsu
2013
Boundary limits of polyharmonic functions in Sobolev-Orlicz spaces. Zbl 0845.31002
Mizuta, Yoshihiro
1995
Hyperplane means of potentials. Zbl 0858.31007
Mizuta, Yoshihiro
1996
Lindelöf theorems for monotone Sobolev functions. Zbl 1035.31005
Futamura, Toshihide; Mizuta, Yoshihiro
2003
Growth properties of $$p$$-th hyperplane means of Green potentials in a half space. Zbl 0757.31003
Mizuta, Yoshihiro
1992
Spherical means of Beppo Levi functions. Zbl 0773.31005
Mizuta, Yoshihiro
1992
Integral representations of Beppo Levi functions and the existence of limits at infinity. Zbl 0702.31006
Mizuta, Yoshihiro
1989
Boundary behavior of p-precise functions on a half space of $$R^ n$$. Zbl 0705.31004
Mizuta, Yoshihiro
1988
On the order at infinity of Riesz potentials. Zbl 0421.31005
Kurokawa, Takahide; Mizuta, Yoshihiro
1979
On the existence of limits along lines of Beppo Levi functions. Zbl 0604.31007
Mizuta, Yoshihiro
1986
Boundary limits of Green potentials of general order. Zbl 0659.31007
Mizuta, Yoshihiro
1987
On the boundary limits of harmonic functions. Zbl 0664.31007
Mizuta, Yoshihiro
1988
Hardy’s inequality in Musielak-Orlicz-Sobolev spaces. Zbl 1316.46030
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2014
Mean continuity for potentials of functions in Musielak-Orlicz spaces. Zbl 1303.46022
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2013
Orlicz-Sobolev capacity of balls. Zbl 1277.46016
Futamura, T.; Mizuta, Y.; Ohno, T.; Shimomura, T.
2011
Variable exponent spaces on metric measure spaces. Zbl 1189.46027
Futamura, Toshihide; Harjulehto, Petteri; Hästö, Peter; Mizuta, Yoshihiro; Shimomura, Tetsu
2009
Riesz decomposition for superbiharmonic functions in the unit ball. Zbl 1184.31009
Futamura, T.; Kitaura, K.; Mizuta, Y.
2009
Riesz decomposition for super-polyharmonic functions in the punctured unit ball. Zbl 1299.31004
Futamura, Toshihide; Mizuta, Yoshihiro; Ohno, Takao
2014
On the boundary limits of Green potentials of functions. Zbl 0695.31006
Mizuta, Yoshihiro
1988
An integral representation and fine limits at infinity for functions whose Laplacians iterated $$m$$ times are measures. Zbl 0893.31007
Mizuta, Yoshihiro
1997
Remarks on the results by Koskela concerning the radial uniqueness for Sobolev functions. Zbl 0890.31005
Mizuta, Yoshihiro
1998
The gradient of a convex function on a regular functional space and its potential theoretic properties. Zbl 0347.47029
1974
Potential theoretic properties of the gradient of a convex function on a functional space. Zbl 0347.47030
1975
Boundary limits of functions in weighted Lebesgue or Sobolev classes. Zbl 1049.31007
Mizuta, Yoshihiro
2001
On the behavior of potentials near a hyperplane. Zbl 0537.31006
Mizuta, Yoshihiro
1983
On the existence of weighted boundary limits of harmonic functions. Zbl 0715.31002
Mizuta, Yoshihiro
1990
Fine differentiability of Riesz potentials. Zbl 0398.31005
Mizuta, Yoshihiro
1978
Spherical means and Riesz decomposition for superbiharmonic functions. Zbl 1103.31004
Kitaura, Keiji; Mizuta, Yoshihiro
2006
Continuity of weakly monotone Sobolev functions of variable exponent. Zbl 1119.31002
Futamura, Toshihide; Mizuta, Yoshihiro
2006
Existence of tangential limits for $$\alpha$$-harmonic functions on half spaces. Zbl 1101.31005
Mizuta, Yoshihiro
2006
On the behavior at infinity of Green potentials in a half space. Zbl 0451.31010
Mizuta, Yoshihiro
1980
Hardy’s inequality in Orlicz-Sobolev spaces of variable exponent. Zbl 1227.46023
Mizuta, Yoshihiro; Nakai, Eiichi; Ohno, Takao; Shimomura, Tetsu
2011
Iterated maximal functions in variable exponent Lebesgue spaces. Zbl 1230.46025
Harjulehto, Petteri; Hästö, Peter; Mizuta, Yoshihiro; Shimomura, Tetsu
2011
Capacity for potentials of functions in Musielak-Orlicz spaces. Zbl 1238.46020
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2011
Variable exponent weighted norm inequality for generalized Riesz potentials. Zbl 1393.46023
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Shimomura, Tetsu
2018
Sobolev’s theorem for double phase functionals. Zbl 1453.46021
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2020
Boundary growth of Sobolev functions for double phase functionals. Zbl 1439.31007
Mizuta, Yoshihiro; Shimomura, Tetsu
2020
Campanato-Morrey spaces for the double phase functionals with variable exponents. Zbl 1441.31004
Mizuta, Yoshihiro; Nakai, Eiichi; Ohno, Takao; Shimomura, Tetsu
2020
Campanato-Morrey spaces for the double phase functionals. Zbl 1452.31010
Mizuta, Yoshihiro; Nakai, Eiichi; Ohno, Takao; Shimomura, Tetsu
2020
Sobolev’s inequality for double phase functionals with variable exponents. Zbl 1423.46049
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2019
Weak estimates for the maximal and Riesz potential operators in non-homogeneous central Herz-Morrey spaces. Zbl 1421.31014
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2019
Sobolev inequalities for Musielak-Orlicz spaces. Zbl 1392.46037
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2018
Variable exponent weighted norm inequality for generalized Riesz potentials on the unit ball. Zbl 1405.46023
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Shimomura, Tetsu
2018
Growth properties of potentials in central Morrey-Orlicz spaces on the unit ball. Zbl 1396.31004
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2018
Variable exponent weighted norm inequality for generalized Riesz potentials. Zbl 1393.46023
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Shimomura, Tetsu
2018
Duality of non-homogeneous central Herz-Morrey-Musielak-Orlicz spaces. Dedicated to Professor Hiroaki Aikawa on the occasion of his sixtieth birthday. Zbl 1387.46029
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2017
Growth properties for Riesz potentials of functions in weighted variable $$L^{p(\cdot)}$$ spaces. Zbl 1375.31008
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2017
Herz-Morrey spaces of variable exponent, Riesz potential operator and duality. Zbl 1312.31013
Mizuta, Yoshihiro; Ohno, Takao
2015
Growth properties of Musielak-Orlicz integral means for Riesz potentials. Zbl 1333.46030
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Shimomura, Tetsu
2015
Weighted Morrey spaces of variable exponent and Riesz potentials. Zbl 1318.31009
Mizuta, Yoshihiro; Shimomura, Tetsu
2015
Sobolev and Trudinger type inequalities on grand Musielak-Orlicz-Morrey spaces. Zbl 1327.31017
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2015
Boundedness of maximal operators and Sobolev’s theorem for non-homogeneous central Morrey spaces of variable exponent. Zbl 1334.31004
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2015
Boundedness of the maximal operator and Sobolev’s inequality on non-homogeneous central Herz-Morrey-Orlicz spaces. Zbl 1325.31002
Mizuta, Yoshihiro; Ohno, Takao
2015
Optimal estimates for the fractional Hardy operator. Zbl 1328.47049
Mizuta, Yoshihiro; Nekvinda, Aleš; Shimomura, Tetsu
2015
Sobolev’s theorem and duality for Herz-Morrey spaces of variable exponent. Zbl 1288.31010
Mizuta, Yoshihiro; Ohno, Takao
2014
Trudinger’s exponential integrability for Riesz potentials of functions in generalized grand Morrey spaces. Zbl 1305.42017
Mizuta, Yoshihiro; Ohno, Takao
2014
Sobolev’s theorem for Riesz potentials of functions in grand Morrey spaces of variable exponent. Zbl 1332.31007
Futamura, Toshihide; Mizuta, Yoshihiro; Ohno, Takao
2014
Hardy’s inequality in Musielak-Orlicz-Sobolev spaces. Zbl 1316.46030
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2014
Riesz decomposition for super-polyharmonic functions in the punctured unit ball. Zbl 1299.31004
Futamura, Toshihide; Mizuta, Yoshihiro; Ohno, Takao
2014
Boundedness of maximal operators and Sobolev’s inequality on Musielak-Orlicz-Morrey spaces. Zbl 1267.46045
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2013
Approximate identities and Young type inequalities in Musielak-Orlicz spaces. Zbl 1313.46041
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2013
Trudinger’s inequality and continuity of potentials on Musielak-Orlicz-Morrey spaces. Zbl 1268.46024
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2013
Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials. Zbl 1269.31005
Mizuta, Yoshihiro; Nakai, Eiichi; Sawano, Yoshihiro; Shimomura, Tetsu
2013
Hardy averaging operator on generalized Banach function spaces and duality. Zbl 1286.47030
Mizuta, Yoshihiro; Nekvinda, Aleš; Shimomura, Tetsu
2013
Mean continuity for potentials of functions in Musielak-Orlicz spaces. Zbl 1303.46022
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2013
Maximal functions, Riesz potentials and Sobolev embeddings on Musielak-Orlicz-Morrey spaces of variable exponent in $$\mathbb{R}^n$$. Zbl 1273.31005
Mizuta, Yoshihiro; Nakai, Eiichi; Ohno, Takao; Shimomura, Tetsu
2012
Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces. Zbl 1246.46034
Mizuta, Yoshihiro; Nakai, Eiichi; Sawano, Yoshihiro; Shimomura, Tetsu
2012
Weighted Sobolev inequality in Musielak-Orlicz space. Zbl 1243.46020
Mizuta, Yoshihiro; Shimomura, Tetsu
2012
Orlicz capacity of balls. Zbl 1316.46031
Mizuta, Yoshihiro; Ohno, Takao
2012
Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents. Zbl 1228.31004
Mizuta, Yoshihiro; Nakai, Eiichi; Ohno, Takao; Shimomura, Tetsu
2011
Orlicz-Sobolev capacity of balls. Zbl 1277.46016
Futamura, T.; Mizuta, Y.; Ohno, T.; Shimomura, T.
2011
Hardy’s inequality in Orlicz-Sobolev spaces of variable exponent. Zbl 1227.46023
Mizuta, Yoshihiro; Nakai, Eiichi; Ohno, Takao; Shimomura, Tetsu
2011
Iterated maximal functions in variable exponent Lebesgue spaces. Zbl 1230.46025
Harjulehto, Petteri; Hästö, Peter; Mizuta, Yoshihiro; Shimomura, Tetsu
2011
Capacity for potentials of functions in Musielak-Orlicz spaces. Zbl 1238.46020
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2011
A Montel type result for super-polyharmonic functions on $$\mathbb{R}^N$$. Zbl 1210.31003
Futamura, Toshihide; Kitaura, Keiji; Mizuta, Yoshihiro
2011
Sobolev’s inequality for Riesz potentials in Orlicz-Musielak spaces of variable exponent. Zbl 1294.46037
Mizuta, Yoshihiro; Nakai, Eiichi; Ohno, Takao; Shimomura, Tetsu
2011
Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials. Zbl 1200.26007
Mizuta, Yoshihiro; Nakai, Eiichi; Ohno, Takao; Shimomura, Tetsu
2010
Compact embeddings for Sobolev spaces of variable exponents and existence of solutions for nonlinear elliptic problems involving the $$p(x)$$-Laplacian and its critical exponent. Zbl 1202.46034
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu; Shioji, Naoki
2010
Continuity properties for Riesz potentials of functions in Morrey spaces of variable exponent. Zbl 1184.31005
Mizuta, Yoshihiro; Shimomura, Tetsu
2010
Approximate identities and Young type inequalities in variable Lebesgue-Orlicz spaces $$L^{p(\cdot)}(\log L)^{q(\cdot)}$$. Zbl 1216.46025
Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao
2010
Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent. Zbl 1193.46016
Futamura, Toshihide; Mizuta, Yoshihiro; Shimomura, Tetsu
2010
Sobolev inequalities for Orlicz spaces of two variable exponents. Zbl 1206.46035
Hästö, Peter; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2010
Sobolev embeddings for Riesz potential spaces of variable exponents near 1 and Sobolev’s exponent. Zbl 1192.46027
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2010
Sobolev’s inequality for Riesz potentials of functions in Morrey spaces of integral form. Zbl 1211.46026
Mizuta, Yoshihiro; Shimomura, Tetsu
2010
Weighted Orlicz-Riesz capacity of balls. Zbl 1219.46034
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2010
Continuity properties of Riesz potentials of Orlicz functions. Zbl 1181.46026
Mizuta, Yoshihiro; Shimomura, Tetsu
2009
Sobolev’s inequality for Riesz potentials of functions in non-doubling Morrey spaces. Zbl 1186.31003
Mizuta, Yoshihiro; Shimomura, Tetsu; Sobukawa, Takuya
2009
Variable exponent spaces on metric measure spaces. Zbl 1189.46027
Futamura, Toshihide; Harjulehto, Petteri; Hästö, Peter; Mizuta, Yoshihiro; Shimomura, Tetsu
2009
Riesz decomposition for superbiharmonic functions in the unit ball. Zbl 1184.31009
Futamura, T.; Kitaura, K.; Mizuta, Y.
2009
Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent. Zbl 1161.46305
Mizuta, Yoshihiro; Shimomura, Tetsu
2008
Sobolev’s inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space $$L^{p(\cdot)}(\log L)^{q(\cdot)}$$. Zbl 1153.31002
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2008
An elementary proof of Sobolev embeddings for Riesz potentials of functions in Morrey spaces $$L^{1,\nu,\beta}(G)$$. Zbl 1175.31005
Mizuta, Yoshihiro; Nakai, Eiichi; Ohno, Takao; Shimomura, Tetsu
2008
Integrability of maximal functions for generalized Lebesgue spaces with variable exponent. Zbl 1143.46010
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2008
Isolated singularities, growth of spherical means and Riesz decomposition for superbiharmonic functions. Zbl 1161.31302
Futamura, Toshihide; Kitaura, Keiji; Mizuta, Yoshihiro
2008
Integrability of maximal functions for generalized Lebesgue spaces $$L^{p(\cdot)}(\log L)^{q(\cdot)}$$. Zbl 1199.46076
Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu
2008
Vanishing exponential integrability for Riesz potentials of functions in Orlicz classes. Zbl 1152.31003
Mizuta, Yoshihiro; Shimomura, Tetsu
2007
Sobolev embeddings for variable exponent Riesz potentials on metric spaces. Zbl 1100.31002
Futamura, Toshihide; Mizuta, Yoshihiro; Shimomura, Tetsu
2006
Sobolev embeddings for Riesz potential space of variable exponent. Zbl 1109.31004
Futamura, Toshihide; Mizuta, Yoshihiro; Shimomura, Tetsu
2006
Maximal functions for Lebesgue spaces with variable exponent approaching 1. Zbl 1111.46019
Futamura, Toshihide; Mizuta, Yoshihiro
2006
Maximal functions, Riesz potentials and Sobolev’s inequality in generalized Lebesgue spaces. Zbl 1125.31001
Mizuta, Yoshihiro; Shimomura, Tetsu
2006
Spherical means and Riesz decomposition for superbiharmonic functions. Zbl 1103.31004
Kitaura, Keiji; Mizuta, Yoshihiro
2006
Continuity of weakly monotone Sobolev functions of variable exponent. Zbl 1119.31002
Futamura, Toshihide; Mizuta, Yoshihiro
2006
Existence of tangential limits for $$\alpha$$-harmonic functions on half spaces. Zbl 1101.31005
Mizuta, Yoshihiro
2006
Continuity properties of Riesz potentials for function in $$L^{p(.)}$$ of variable exponent. Zbl 1087.31004
Futamura, Toshihide; Mizuta, Yoshihiro
2005
Sobolev’s inequality for Riesz potentials with variable exponent satisfying a log-Hölder condition at infinity. Zbl 1085.31005
Mizuta, Yoshihiro; Shimomura, Tetsu
2005
Boundary behavior of monotone Sobolev functions on John domains in a metric space. Zbl 1074.31005
Futamura, Toshihide; Mizuta, Yoshihiro
2005
Continuity of weakly monotone Sobolev functions. Zbl 1101.46021
Futamura, Toshihide; Mizuta, Yoshihiro
2005
Continuity of Sobolev functions of variable exponent on metric spaces. Zbl 1072.46506
Mizuta, Yoshihiro; Shimomura, Tetsu
2004
Isolated singularities of super-polyharmonic functions. Zbl 1073.31005
Futamura, Toshihide; Mizuta, Yoshihiro
2004
Growth properties for modified Poisson integrals in a half space. Zbl 1056.31004
Mizuta, Yoshihiro; Shimomura, Tetsu
2004
Removability of sets for sub-polyharmonic functions. Zbl 1041.31004
Futamura, Toshihide; Kishi, Kyoko; Mizuta, Yoshihiro
2003
Lindelöf theorems for monotone Sobolev functions. Zbl 1035.31005
Futamura, Toshihide; Mizuta, Yoshihiro
2003
On semi-fine limits at infinity for Riesz potentials and monotone BLD functions. Zbl 1033.31003
Mizuta, Yoshihiro; Shimomura, Tetsu
2003
Tangential limits and removable sets for weighted Sobolev spaces. Zbl 1030.31006
Futamura, Toshihide; Mizuta, Yoshihiro
2003
Radial growth of $$C^2$$ functions satisfying Bloch type condition. Zbl 1060.31003
Futamura, Toshihide; Mizuta, Yoshihiro
2003
Continuity and differentiability for weighted Sobolev spaces. Zbl 1029.46032
Mizuta, Yoshihiro; Shimomura, Tetsu
2002
Crack edge element of three-dimensional displacement discontinuity method with boundary division into triangular leaf elements. Zbl 1052.74586
Li, H.; Liu, C. L.; Mizuta, Y.; Kayupov, M. A.
2001
A generalization of Bôcher’s theorem for polyharmonic functions. Zbl 1013.31005
Futamura, Toshihide; Kishi, Kyoko; Mizuta, Yoshihiro
2001
Boundary limits of functions in weighted Lebesgue or Sobolev classes. Zbl 1049.31007
Mizuta, Yoshihiro
2001
A generalization of the Liouville theorem to polyharmonic functions. Zbl 0977.31005
Futamura, Toshihide; Kishi, Kyoko; Mizuta, Yoshihiro
2001
Differentiability and Hölder continuity of Riesz potentials of Orlicz functions. Zbl 0955.31002
Mizuta, Yoshihiro; Shimomura, Tetsu
2000
Growth properties of spherical means for monotone BLD functions in the unit ball. Zbl 0956.31005
Mizuta, Yoshihiro; Shimomura, Tetsu
2000
Boundary limits of spherical means for BLD and monotone BLD functions in the unit ball. Zbl 0926.31003
Mizuta, Yoshihiro; Shimomura, Tetsu
1999
Exponential integrability for Riesz potentials of functions in Orlicz classes. Zbl 0917.31004
Mizuta, Yoshihiro; Shimomura, Tetsu
1998
Remarks on the results by Koskela concerning the radial uniqueness for Sobolev functions. Zbl 0890.31005
Mizuta, Yoshihiro
1998
Integral representations, differentiability properties and limits at infinity for Beppo Levi functions. Zbl 0885.31004
Mizuta, Yoshihiro
1997
An integral representation and fine limits at infinity for functions whose Laplacians iterated $$m$$ times are measures. Zbl 0893.31007
Mizuta, Yoshihiro
1997
Hyperplane means of potentials. Zbl 0858.31007
Mizuta, Yoshihiro
1996
On the existence of tangential limits of monotone BLD functions. Zbl 0866.31004
Matsumoto, Shigeki; Mizuta, Yoshihiro
1996
Potential theory in Euclidean spaces. Zbl 0849.31001
Mizuta, Yoshihiro
1995
Tangential limits of monotone Sobolev functions. Zbl 0852.31008
Mizuta, Yoshihiro
1995
Taylor expansion of Riesz potentials. Zbl 0863.31005
Shimomura, Tetsu; Mizuta, Yoshihiro
1995
Boundary limits of polyharmonic functions in Sobolev-Orlicz spaces. Zbl 0845.31002
Mizuta, Yoshihiro
1995
A theorem of Hardy-Littlewood for harmonic functions satisfying Hölder’s condition. Zbl 0842.31003
Kiso, Toshihiro; Mizuta, Yoshihiro; Shimomura, Tetsu
1995
Continuity properties of potentials and Beppo-Levi-Deny functions. Zbl 0782.31004
Mizuta, Yoshihiro
1993
...and 30 more Documents
all top 5

#### Cited by 278 Authors

 82 Shimomura, Tetsu 67 Mizuta, Yoshihiro 48 Ohno, Takao 27 Sawano, Yoshihiro 18 Hästö, Peter A. 14 Nakai, Eiichi 13 Harjulehto, Petteri 13 Maeda, Fumiyuki 11 Guliyev, Vagif Sabir 9 Futamura, Toshihide 8 Samko, Stefan Grigorievich 6 Fiorenza, Alberto 6 Hasanov, Javanshir J. 5 Chlebicka, Iwona 5 Cruz-Uribe, David Vincente 5 Górka, Przemysław 5 Ho, Kwok-Pun 5 Saintier, Nicolas 5 Silva, Analía 4 Badalov, Xayyam A. 4 Deringoz, Fatih 4 Fernández Bonder, Julián 4 Gwiazda, Piotr 4 Latvala, Visa 4 Sugiyama, Yuusuke 4 Yamamoto, Masakazu 4 Yang, Dachun 4 Zatorska-Goldstein, Anna 3 Almeida, Alexandre 3 Anatriello, Giuseppina 3 Deng, Guantie 3 Formica, Maria Rosaria 3 Fu, Zunwei 3 Giannetti, Flavia 3 Hurri-Syrjānen, Ritva 3 Karppinen, Arttu 3 Riihentaus, Juhani 3 Shen, Baotang 3 Shi, Jingyu 3 Taliaferro, Steven D. 3 Villamor, Enrique 3 Xu, Bochi 2 Akagi, Goro 2 Anandam, Victor 2 Aykol, Canay 2 Bandaliev, Rovshan Alifaga ogly 2 Bilogliadov, Mykhailo 2 Brigante, Michele 2 Caetano, António M. 2 Cianchi, Andrea 2 Colasuonno, Francesca 2 Dorronsoro, José R. 2 Edmunds, David Eric 2 Fan, Xianling 2 Fu, Yongqiang 2 Gaczkowski, Michał 2 Ghergu, Marius 2 Gogatishvili, Amiran 2 Hussain, Amjad 2 Manfredi, Juan J. 2 Matsuoka, Katsuo 2 Miklyukov, Vladimir Mikhaiĭlovich 2 Najafov, Alik M. 2 Pucci, Patrizia 2 Qiao, Lei 2 Render, Hermann 2 Sarfraz, Naqash 2 Shi, Minglei 2 Stoll, Manfred 2 Sumbatyan, Mezhlum A. 2 Tanaka, Hitoshi 2 Tian, Boping 2 Vuorinen, Matti Keijo Kustaa 2 Wang, Hongbin 2 Xiong, Jingang 2 Yamauchi, Yusuke 2 Zhuo, Ciqiang 1 Abdelkefi, Chokri 1 Adams, David Randolph 1 Ahern, Patrick B. 1 Ahmida, Youssef 1 Akgun, Ramazan 1 Al-Gwaiz, Mohammed A. 1 Alberico, Angela 1 Alekberli, Sain T. 1 Alisoy, G. T. 1 Alisoy, Hafiz Z. 1 Arai, Ryutaro 1 Attouch, Hedy 1 Autuori, Giuseppina 1 Baalal, Azeddine 1 Babayev, Rovshan F. 1 Baratchart, Laurent 1 Barilla, David 1 Baroni, Paolo 1 Batbold, Tserendorj 1 Ben Chrouda, Mohamed 1 Ben Fredj, Mahmoud 1 Benyaiche, Allami 1 Berghout, Mohamed ...and 178 more Authors
all top 5

#### Cited in 117 Serials

 27 Journal of Mathematical Analysis and Applications 17 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Potential Analysis 10 Complex Variables and Elliptic Equations 9 Annales Academiae Scientiarum Fennicae. Mathematica 8 Journal of Functional Analysis 7 Journal of Differential Equations 7 Proceedings of the American Mathematical Society 7 Transactions of the American Mathematical Society 7 Engineering Analysis with Boundary Elements 6 Mathematische Nachrichten 6 Tohoku Mathematical Journal. Second Series 6 Revista Matemática Complutense 5 Czechoslovak Mathematical Journal 5 Journal of the Mathematical Society of Japan 4 Integral Equations and Operator Theory 4 Manuscripta Mathematica 4 Journal of Inequalities and Applications 4 Mathematical Inequalities & Applications 4 Journal of Function Spaces and Applications 4 Journal of Function Spaces 3 Collectanea Mathematica 3 Illinois Journal of Mathematics 3 Proceedings of the Japan Academy. Series A 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Forum Mathematicum 3 The Journal of Geometric Analysis 3 Calculus of Variations and Partial Differential Equations 3 Journal of Mathematical Sciences (New York) 3 NoDEA. Nonlinear Differential Equations and Applications 3 Bulletin des Sciences Mathématiques 3 Integral Transforms and Special Functions 3 Computational Methods and Function Theory 3 Mediterranean Journal of Mathematics 3 Banach Journal of Mathematical Analysis 3 Kyoto Journal of Mathematics 2 Studia Mathematica 2 Annales de l’Institut Fourier 2 Applied Mathematics and Computation 2 Canadian Mathematical Bulletin 2 Colloquium Mathematicum 2 Duke Mathematical Journal 2 Osaka Journal of Mathematics 2 Ricerche di Matematica 2 Zeitschrift für Analysis und ihre Anwendungen 2 Georgian Mathematical Journal 2 The Journal of Fourier Analysis and Applications 2 Abstract and Applied Analysis 2 Positivity 2 Communications in Contemporary Mathematics 2 Lobachevskii Journal of Mathematics 2 Journal of the Australian Mathematical Society 2 Frontiers of Mathematics in China 2 Journal of Mathematical Inequalities 2 Science China. Mathematics 2 Analysis and Mathematical Physics 1 Analysis Mathematica 1 Applicable Analysis 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 Indian Journal of Pure & Applied Mathematics 1 Israel Journal of Mathematics 1 Journal d’Analyse Mathématique 1 Journal of the Mechanics and Physics of Solids 1 Mathematical Methods in the Applied Sciences 1 Mathematical Notes 1 Nonlinearity 1 Periodica Mathematica Hungarica 1 Arkiv för Matematik 1 Acta Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Archiv der Mathematik 1 Compositio Mathematica 1 Dissertationes Mathematicae 1 Glasgow Mathematical Journal 1 Hiroshima Mathematical Journal 1 Indiana University Mathematics Journal 1 Journal of Approximation Theory 1 Journal für die Reine und Angewandte Mathematik 1 Kodai Mathematical Journal 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 Nagoya Mathematical Journal 1 Quaestiones Mathematicae 1 Revista de la Unión Matemática Argentina 1 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 1 Complex Variables. Theory and Application 1 Acta Applicandae Mathematicae 1 Constructive Approximation 1 Applied Mathematics Letters 1 Asymptotic Analysis 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Applied Mathematics. Series B (English Edition) 1 St. Petersburg Mathematical Journal 1 Taiwanese Journal of Mathematics 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Fractional Calculus & Applied Analysis 1 Acta Mathematica Sinica. English Series ...and 17 more Serials
all top 5

#### Cited in 27 Fields

 181 Functional analysis (46-XX) 106 Potential theory (31-XX) 98 Harmonic analysis on Euclidean spaces (42-XX) 59 Partial differential equations (35-XX) 29 Real functions (26-XX) 17 Operator theory (47-XX) 15 Functions of a complex variable (30-XX) 11 Mechanics of deformable solids (74-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 6 Approximations and expansions (41-XX) 6 Numerical analysis (65-XX) 5 Several complex variables and analytic spaces (32-XX) 4 Probability theory and stochastic processes (60-XX) 3 Integral transforms, operational calculus (44-XX) 3 Differential geometry (53-XX) 3 Fluid mechanics (76-XX) 2 Measure and integration (28-XX) 2 Integral equations (45-XX) 2 Geophysics (86-XX) 1 Algebraic geometry (14-XX) 1 Ordinary differential equations (34-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Information and communication theory, circuits (94-XX)