Sharp embedding relations between Local Hardy and $\alpha$-Modulation Spaces

TL;DR

This paper establishes the optimal embedding relations between local Hardy spaces and lpha-modulation spaces, extending previous results on local Hardy and modulation space embeddings to a broader class of spaces.

Contribution

It provides the first comprehensive characterization of embeddings between local Hardy and lpha-modulation spaces, generalizing earlier work on local Hardy and modulation spaces.

Findings

Derived optimal embedding conditions between local Hardy and lpha-modulation spaces.

Extended known embedding results from modulation spaces to lpha-modulation spaces.

Unified the understanding of space relations in harmonic analysis.

Abstract

We give the optimal embedding relations between local Hardy space and $\alpha$-modulation spaces, which extend the results for the embedding relations between local Hardy and modulation spaces obtained by Kobayashi, Miyachi and Tomita in [Studia Math. 192 (2009), 79-96].