Characterization of inclusion relations between Wiener amalgam and some classical spaces

Abstract

In this paper, we establish the sharp conditions for the inclusion relations between Besov spaces Bp,q and Wiener amalgam spaces W s p,q . We also obtain the optimal inclusion relations between local hardy spaces h p and Wiener amalgam spaces W s p,q , 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.2000 Mathematics Subject Classification. 42B35.

Hausdorff operators on modulation and Wiener amalgam spaces

“…We refer the reader to [5] for some motivations and historical remarks. One can also refer our recent paper [8,9] for the properties of modulation spaces and Wiener amalgam spaces.…”

The unboundedness of Hausdorff operators on quasi‐Banach spaces

“…is equal to the Wiener amalgam space W p, q (see Guo et al, 21 p. 10), and recall the embedding relations (see lemma 2.5 of Guo et al 22 ):…”

The unboundedness of Hausdorff operators on Quasi-Banach spaces

“…By the conclusion for Y = M p,∞ , we have ϕ * f L p f M p,∞ . Note that F M q,p is equal to the Wiener amalgam space W p,q (see [11, pp.10]), and recall the embedding relations (see [10,Lemma 2.5]):…”