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Embeddings of some classical Banach spaces into modulation spaces

Authors:	Kasso A. Okoudjou

Affiliation:	School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160

Abstract:	We give sufficient conditions for a tempered distribution to belong to certain modulation spaces by showing embeddings of some Besov-Triebel-Lizorkin spaces into modulation spaces. As a consequence we have a new proof that the Hölder-Lipschitz space $C^{s}(mathbb{R} ^{d})$ embeds into the modulation space $M^{infty,1}(mathbb{R} ^{d})$ when . This embedding plays an important role in interpreting recent modulation space approaches to pseudodifferential operators.

Keywords:	Besov space modulation space Sobolev space short-time Fourier transform Triebel-Lizorkin space time-frequency analysis

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