On embeddings of Morrey type spaces between weighted Lebesgue or Stummel spaces with application to Herz spaces

Humberto Rafeiro, Stefan Samko

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We study embeddings of Morrey type spaces Mp,q,ω(Rn) , 1 ⩽ p< ∞, 1 ⩽ q< ∞, both local and global, into weighted Lebesgue spaces Lp(Rn, w) , with the main goal to better understand the local behavior of functions f∈ Mp,q,ω(Rn) and also their behavior at infinity. Under some assumptions on the function ω, we prove that the local Morrey type space is embedded into Lp(Rn, w) , where w(r) = ω(r) if q= 1 , and w(r) is “slightly distorted” in comparison with ω(r) if q> 1. In the case q> p we show that the embedding, in general, cannot hold with ω= w. For global Morrey type spaces we also prove embeddings into Stummel spaces. Similar embeddings for complementary Morrey type spaces are obtained. We also study inverse embeddings of weighted Lebesgue spaces Lp(Rn, w) into Morrey type and complementary Morrey type spaces. Finally, using our previous results on relations between Herz and Morrey type spaces, we obtain “for free” similar embeddings for Herz spaces.

Original languageEnglish
Article number48
JournalBanach Journal of Mathematical Analysis
Volume15
Issue number3
DOIs
Publication statusPublished - Jul 2021

Keywords

  • Embeddings
  • Herz spaces
  • Morrey type spaces
  • Stummel spaces
  • Weighted Lebesgue spaces

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

Fingerprint

Dive into the research topics of 'On embeddings of Morrey type spaces between weighted Lebesgue or Stummel spaces with application to Herz spaces'. Together they form a unique fingerprint.

Cite this