Characterization of inclusion relations between wiener amalgam and some classical spaces

TL;DR

This paper determines the precise conditions under which Wiener amalgam spaces include Besov, local Hardy, and Triebel-Lizorkin spaces, extending previous results and connecting modern inequalities with classical ones.

Contribution

It provides sharp and optimal inclusion relations between Wiener amalgam spaces and several classical function spaces, improving and extending prior research.

Findings

Sharp inclusion conditions between Besov and Wiener amalgam spaces.

Optimal inclusion relations between local Hardy and Wiener amalgam spaces.

Characterizations of inclusion relations between Triebel-Lizorkin and Wiener amalgam spaces.

Abstract

In this paper, we establish the sharp conditions for the inclusion relations between Besov spaces $B_{p,q}$ and Wiener amalgam spaces $W_{p,q}^s$. We also obtain the optimal inclusion relations between local hardy spaces $h^p$ and Wiener amalgam spaces $W_{p,q}^s$, which completely improve and extend the main results obtained by Cunanana, Kobayashib and Sugimotoa in [J. Funct. Anal. 268 (2015), 239-254]. In addition, we establish some mild characterizations of inclusion relations between Triebel-Lizorkin and Wiener amalgam spaces, which relates some modern inequalities to classical inequalities.