Hardy spaces associated with different homogeneities and boundedness of composition operators

Yongsheng Han, Chincheng Lin, Guozhen Lu, Zhuoping Ruan, Eric T. Sawyer

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22 Scopus citations

Abstract

It is well known that standard Calderón-Zygmund singular integral operators with isotropic and nonisotropic homogeneities are bounded on the classical Hp(ℝm) and nonisotropic Hh p(ℝm), respectively. In this paper, we develop a new Hardy space theory and prove that the composition of two Calderón-Zygmund singular integral operators with different homogeneities is bounded on this new Hardy space. Such a Hardy space has a multiparameter structure associated with the underlying mixed homogeneities arising from the two singular integral operators under consideration. The Calderón-Zygmund decomposition and an interpolation theorem hold on these new Hardy spaces.

Original languageEnglish
Pages (from-to)1127-1157
Number of pages31
JournalRevista Matematica Iberoamericana
Volume29
Issue number4
DOIs
StatePublished - 2013

Keywords

  • Almost orthogonality estimates
  • Calderón-Zygmund operators
  • Discrete Calderón's identity
  • Discrete Littlewood-Paley-Stein square functions
  • Hardy spaces

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