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December 2010 Molecular decomposition of the modulation spaces
Masaharu Kobayashi, Yoshihiro Sawano
Osaka J. Math. 47(4): 1029-1053 (December 2010).

Abstract

The aim of this paper is to develop a theory of decomposition in the weighted modulation spaces $M_{p,q}^{s,W}$ with $0 < p,q \le \infty$, $s \in \mathbb{R}$ and $W \in A_{\infty}$, where $W$ belongs to the class of $A_{\infty}$ defined by Muckenhoupt. For this purpose we shall define molecules for the modulation spaces. As an application we give a simple proof of the boundedness of the pseudo-differential operators with symbols in $M_{\infty,\min(1,p,q)}^{0}$. We shall deal with dual spaces as well.

Citation

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Masaharu Kobayashi. Yoshihiro Sawano. "Molecular decomposition of the modulation spaces." Osaka J. Math. 47 (4) 1029 - 1053, December 2010.

Information

Published: December 2010
First available in Project Euclid: 20 December 2010

zbMATH: 1211.42021
MathSciNet: MR2791565

Subjects:
Primary: 42B35
Secondary: 41A17

Rights: Copyright © 2010 Osaka University and Osaka City University, Departments of Mathematics

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Vol.47 • No. 4 • December 2010
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