Sharp embedding between Besov-Triebel-Sobolev spaces and modulation spaces

TL;DR

This paper explicitly characterizes the embedding relations between Besov-Triebel-Sobolev spaces and modulation spaces, extending previous results to more general cases and establishing sharp embeddings with Fourier $L^{p}$ spaces.

Contribution

It provides the most general explicit embeddings between these function spaces, extending prior work and including sharp Fourier $L^{p}$ to modulation space embeddings.

Findings

Explicit embedding relations derived

Extended previous results to general cases

Established sharp embeddings with Fourier $L^{p}$ spaces

Abstract

The embedding relations between Besov-Triebel-Sobolev spaces and modulation spaces are determined explicitly. We extend the results of Sugimoto[2007]; Wang[2007] and Kobayashi[2011] to the most general cases. And we give the sharp embedding between Fourier $L^{p}$ spaces and modulation spaces.