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Embeddings of some classical Banach spaces into modulation spaces

Author: Kasso A. Okoudjou
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1639-1647
MSC (2000): Primary 46E35; Secondary 42B35
Published electronically: January 29, 2004
MathSciNet review: 2051124
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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 $s>d$. This embedding plays an important role in interpreting recent modulation space approaches to pseudodifferential operators.

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Additional Information

Kasso A. Okoudjou
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160
Address at time of publication: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York, 14853-4201

Keywords: Besov space, modulation space, Sobolev space, short-time Fourier transform, Triebel-Lizorkin space, time-frequency analysis
Received by editor(s): March 22, 2002
Published electronically: January 29, 2004
Additional Notes: The author was partially supported by NSF Grant DMS-9970524
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society