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

Mitsuo Izuki, Takahiro Noi

Research output: Contribution to journalArticle

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
JournalMathematische Nachrichten
DOIs
Publication statusAccepted/In press - Jan 1 2019

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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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