Osaka Journal of Mathematics

Molecular decomposition of the modulation spaces

Masaharu Kobayashi and Yoshihiro Sawano

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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.

Article information

Osaka J. Math., Volume 47, Number 4 (2010), 1029-1053.

First available in Project Euclid: 20 December 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B35: Function spaces arising in harmonic analysis
Secondary: 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol s kii-type inequalities)


Kobayashi, Masaharu; Sawano, Yoshihiro. Molecular decomposition of the modulation spaces. Osaka J. Math. 47 (2010), no. 4, 1029--1053.

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