The dilation property of modulation spaces and their inclusion relation with Besov spaces

Details The dilation property of modulation spaces and their inclusion relation with Besov spaces The dilation property of modulation spaces and their inclusion relation with Besov spaces

2006-06-08

arxiv.org/abs/math/0606176v1

Mathematics

Functional Analysis

23 pages

Scientific paper

We consider the dilation property of the modulation spaces $M^{p,q}$. Let $D_\lambda:f(t)\mapsto f(\lambda t)$ be the dilation operator, and we consider the behavior of the operator norm $\|D_\lambda\|_{M^{p,q}\to M^{p,q}}$ with respect to $\lambda$. Our result determines the best order for it, and as an application, we establish the optimality of the inclusion relation between the modulation spaces and Besov space, which was proved by Toft.

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