Researcher Information

Masaharu Kobayashi

Associate Professor

Function spaces and operators

Department of Mathematics, Mathematics

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Theme

Function spaces and its applications to PDE

FieldHarmonic Analysis, Real Analysis
KeywordFunction spaces, Time-frequency analysis, Pseudo-differential operators, Schrödinger operators, Singular integral operatos

Introduction of Research

My research field is analysis. Especially, I am interested in topics called harmonic analysis and real analysis. Roughly speaking, to study boundedness, continuity, differentiability and integrability of functions, we measure “quantitative properties” of functions. We also study how these “quantitative properties” change when we apply various operators. To measure “quantitative properties”, we use various norms (and we also use function spaces defined by these norms). Recently, I am interested in the theory of modulation spaces which were introduced by H.Feichtinger, and I’m trying to study pseudo-differential operators and partial differential equations in the framework of modulation spaces.

Representative Achievements

Operating functions on modulation and Wiener amalgam spaces, M. Kobayashi, E. Sato, Nagoya Math. J. 230 72-82, 2018.
Inclusion relations between L p -Sobolev and Wiener amalgam spaces, J.Cunanan, M.Kobayashi, M.Sugimoto, J. Funct. Anal.   268(1) 239-254, 2015.
Estimates on modulation spaces for Schrödinger evolution operators with quadratic and sub-quadratic potentials, K.Kato, M.Kobayashi, S. Ito, J. Funct. Anal.   266(2) 733-753, 2014.
Estimates on modulation spaces for Schrödinger evolution operators with quadratic and sub-quadratic potentials, K.Kato, M.Kobayashi, S. Ito J. Funct. Anal.   266(2) 733-753, 2014.
Modulation spaces M p,q for 0<p,q≤∞, M. Kobayashi, J. Funct. Spaces Appl.   4(3) 329-341, 2006.
Academic degreePh.D.
Affiliated academic societyThe Mathematical Society of Japan