Hardy spaces and the Tb theorem

Yongsheng Han, Ming Yi Lee, Chin Cheng Lin

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

It is well-known that Calderón-Zygmund operators T are bounded on H p for n/n+1 < p ≤ 1 provided T*(1) = 0. In this article, it is shown that if T*(b) = 0, where b is a para-accretive function, T is bounded from the classical Hardy space H p to a new Hardy space H b p . To develop an H b p theory, a discrete Calderón-type reproducing formula and Plancherel-Pôlya- type inequalities associated to a para-accretive function are established. Moreover, David, Journé, and Semmes' result [9] about the L P, 1 < p < ∞, boundedness of the Littlewood-Paley g function associated to a para-accretive function is generalized to the case of p ≤ 1. A new characterization of the classical Hardy spaces by using more general cancellation adapted to para-accretive functions is also given. These results complement the celebrated Calderón-Zygmund operator theory.

Original languageEnglish
Pages (from-to)291-318
Number of pages28
JournalJournal of Geometric Analysis
Volume14
Issue number2
DOIs
StatePublished - 2004

Keywords

  • Calderón-Zygmund operator
  • Hardy space
  • Littlewood-Paley g function
  • Plancherel-Plôya inequality
  • Tb theorem
  • discrete Calderón formula

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