Embeddings of some classical Banach spaces into modulation spaces

Okoudjou, Kasso

doi:10.1090/S0002-9939-04-07401-5

Embeddings of some classical Banach spaces into modulation spaces
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by Kasso A. Okoudjou PDF

Proc. Amer. Math. Soc. 132 (2004), 1639-1647 Request permission

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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