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arXiv · 1606.01386

Full Characterization of embedding relations between alpha modulation spaces

Weichao Guo·Dashan Fan·Huoxiong Wu·Guoping Zhao
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Abstract

In this paper, we consider the embedding relations between any two $\alpha$% -modulation spaces. Based on an observation that the $\alpha$-modulation space with smaller $\alpha$ can be regarded as a corresponding $\alpha$% -modulation space with larger $\alpha$, we give a complete characterization of the Fourier multipliers between $\alpha$-modulation spaces with different $\alpha$. Then we establish a full version of optimal embedding relations between $\alpha$-modulation spaces. As an application, we determine that the bounded operators commuting with translations between $\alpha$-modulation spaces are of convolution type.

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Weichao Guo, Dashan Fan, Huoxiong Wu, Guoping Zhao. 2016-06-04. Full Characterization of embedding relations between alpha modulation spaces. https://arxiv.org/abs/1606.01386

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