Calderón-Zygmund operators on product Hardy spaces

Yongsheng Han, Ming Yi Lee, Chin Cheng Lin, Ying Chieh Lin

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

Let T be a product Calderón-Zygmund singular integral introduced by Journé. Using an elegant rectangle atomic decomposition of Hp (Rn × Rm) and Journé's geometric covering lemma, R. Fefferman proved the remarkable Hp (Rn × Rm) - Lp (Rn × Rm) boundedness of T. In this paper we apply vector-valued singular integral, Calderón's identity, Littlewood-Paley theory and the almost orthogonality together with Fefferman's rectangle atomic decomposition and Journé's covering lemma to show that T is bounded on product Hp (Rn × Rm) for max {frac(n, n + ε), frac(m, m + ε)} < p ≤ 1 if and only if T1* (1) = T2* (1) = 0, where ε is the regularity exponent of the kernel of T.

Original languageEnglish
Pages (from-to)2834-2861
Number of pages28
JournalJournal of Functional Analysis
Volume258
Issue number8
DOIs
StatePublished - 15 Apr 2010

Keywords

  • Calderón-Zygmund operators
  • Journé's class
  • Littlewood-Paley function
  • Product Hardy spaces

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