Inclusion relations between Modulation and Triebel-Lizorkin spaces

TL;DR

This paper establishes precise conditions under which modulation spaces and Triebel-Lizorkin spaces include one another, extending previous results on local Hardy space embeddings.

Contribution

It provides sharp inclusion criteria between modulation and Triebel-Lizorkin spaces for p ≤ 1, improving prior embedding results.

Findings

Sharp inclusion conditions between M_{p,q}^s and F_{p,r} spaces for p ≤ 1

Extended previous results on local Hardy space and modulation space embeddings

Enhanced understanding of the structure of function space relations

Abstract

In this paper, we obtain the sharp conditions of the inclusion relations between modulation spaces $M_{p,q}^s$ and Triebel-Lizorkin spaces $F_{p,r}$ for $p\leq 1$, which greatly improve and extend the results for the embedding relations between local Hardy spaces and modulation spaces obtained by Kobayashi, Miyachi and Tomita in [Studia Math. 192 (2009), 79-96].