Molecular decomposition and a class of Fourier multipliers for bi-parameter modulation spaces

Qing Hong; Guorong Hu

doi:10.3934/cpaa.2019139

Article Contents

2019, Volume 18, Issue 6: 3103-3120. Doi: 10.3934/cpaa.2019139

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$ \mathbb{R}^N $

involving asymptotically linear terms Next Article Invariant measure of stochastic fractional Burgers equation with degenerate noise on a bounded interval

Molecular decomposition and a class of Fourier multipliers for bi-parameter modulation spaces

Qing Hong and
Guorong Hu^,

Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330022, China

^* Corresponding author
^* Corresponding author

Received: September 30, 2018

Revised: January 31, 2019

Published: May 2019

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Abstract

In this paper, we investigate bi-parameter modulation spaces on the product of two Euclidean spaces $ \mathbb{R}^{n} $ and $ \mathbb{R}^{m} $ via uniform decompositions of each factor. A molecular decomposition of these bi-parameter spaces are given, which generalizes the related single-parameter result of Kobayashi and Sawano [33]. Furthermore, we prove the boundedness of a class of Fourier multipliers on bi-parameter modulation spaces, generalizing the results of Bényi et al. [2] and Feichtinger and Narimani [17].

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Mathematics Subject Classification: Primary: 42B35, 42B25; Secondary: 42B15.

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