Carleson measure spaces associated to para-accretive functions

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Abstract

To study the boundedness of the Cauchy integrals over Lipschitz curves, new Hardy spaces H b p were introduced in [Y. Han, M.-Y. Lee and C.-C. Lin, Hardy spaces and the Tb theorem, J. Geom. Anal. 14 (2004) 291318], where b is a para-accretive function. In this paper, we define the Carleson measure spaces CMO b p that generalize BMO, and show that CMO b p is the dual space of H b p. As an application, we give a Carleson measure characterization of BMO b.

Original languageEnglish
Article number1250002
JournalCommunications in Contemporary Mathematics
Volume14
Issue number1
DOIs
StatePublished - Feb 2012

Keywords

  • Approximation to the identity
  • Carleson measure space
  • Hardy space
  • para-accretive function
  • PlancherelPô;lya inequality

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