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arXiv · 1804.00948

Compactness properties for modulation spaces

Christine Pfeuffer·Joachim Toft
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Abstract

We prove that if $ω_1$ and $ω_2$ are moderate weights and $\mascB$ is a suitable (quasi-)Banach function space, then a necessary and sufficient condition for the embedding $i\, :\, M (ω_1,\mascB )\to M (ω_2,\mascB )$ between two modulation spaces to be compact is that the quotient $ω_2/ω_1$ vanishes at infinity. Moreover we show, that the boundedness of $ω_2/ω_1$ a necessary and sufficient condition for the previous embedding to be continuous.

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Christine Pfeuffer, Joachim Toft. 2018-04-03. Compactness properties for modulation spaces. https://arxiv.org/abs/1804.00948

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