Triebel-lizorkin spaces of para-accretive type and a T b theorem

Chin Cheng Lin, Kunchuan Wang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In this article, we use a discrete Calderón-type reproducing formula and Plancherel-Pôlya-type inequality associated to a para-accretive function to characterize the Triebel-Lizorkin spaces of para-accretive type F· a,q b,p , which reduces to the classical Triebel-Lizorkin spaces when the para-accretive function is constant. Moreover, we give a necessary and sufficient condition for the F· 0,q 1,p -F· 0,q b,p boundedness of paraproduct operators. From this, we show that a generalized singular integral operator T with MbTMb ε WBP is bounded from F· 0,q 1,p to F· 0,q b,p if and only if T b ε F· 0,q b,∞ and T *b = 0 for n/n+e <p = 1 and n/ n+e <q ≤ 2, where e is the regularity exponent of the kernel of T.

Original languageEnglish
Pages (from-to)667-694
Number of pages28
JournalJournal of Geometric Analysis
Volume19
Issue number3
DOIs
StatePublished - Jul 2009

Keywords

  • Calderón reproducing formula
  • Para-accretive function
  • Paraproduct operator
  • Plancherel-Pôlya inequality
  • T b theorem
  • Triebel-Lizorkin space

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