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Title: Generalized Campanato spaces with variable growth condition (Harmonic Analysis and Nonlinear Partial Differential Equations)
Authors: Nakai, Eiichi
Keywords: 42B35
46E30
42B20
42B25
Campanato space
Morrey space
variable growth condition
singular integral
fractional integral
commutator
Issue Date: Apr-2019
Publisher: Research Institute for Mathematical Sciences, Kyoto University
Journal title: 数理解析研究所講究録別冊 = RIMS Kokyuroku Bessatsu
Volume: B74
Start page: 65
End page: 92
Abstract: This is a survey on generalized Campanato spaces with variable growth condition. We first define generalized Campanato spaces and related function spaces. Then we state the relations among these function spaces and the characterization of pointwise multipliers on generalized Campanato spaces. Next we state the boundedness of singular integral operators and the convolution operator with the heat kernel. We also give an application of generalized Campanato spaces to the Cauchy problem for the Navier‐Stokes equation. Finally, we state the boundedness of the commutators generated by functions in generalized Campanato spaces.
Description: "Harmonic Analysis and Nonlinear Partial Differential Equations". June 25-27, 2018. edited by Hideo Takaoka and Satoshi Masaki. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.
Rights: © 2019 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.
URI: http://hdl.handle.net/2433/244762
Appears in Collections:B74 Harmonic Analysis and Nonlinear Partial Differential Equations

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