Generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on domains

Mitsuo Izuki, Takahiro Noi

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider a non-smooth atomic decomposition by using a smooth atomic decomposition. Applying the non-smooth atomic decomposition, a local means characterization and a quarkonical decomposition, we obtain a pointwise multiplier and a trace operator for generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on the whole space. We also develop the theory of those spaces on domains. We consider an extension operator and a trace operator on the upper half space and on compact oriented Riemannian manifolds.

Original languageEnglish
Pages (from-to)2212-2251
Number of pages40
JournalMathematische Nachrichten
Volume292
Issue number10
DOIs
Publication statusPublished - Oct 1 2019

Keywords

  • Besov space
  • Morrey space
  • Primary: 42B35; Secondary: 41A17
  • Triebel–Lizorkin space
  • non-smooth atomic decomposition
  • trace operator

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on domains'. Together they form a unique fingerprint.

Cite this