Boundedness of singular integrals with flag kernels on weighted flag hardy spaces

Yongsheng Han, Chin Cheng Lin, Xinfeng Wu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We establish a weighted Hardy space theory associated with flag structures. This theory differs from those in the classical one-parameter and the product settings, and includes weighted Hardy spaces H p F,w, weighted Carleson measure spaces CMOp F,w (the dual spaces of H p F,w), and the boundedness of singular integrals with flag kernels on these spaces. We also derive a Calderón-Zygmund decomposition and provide interpolation of operators acting on H p F,w. Examples and counterexamples are constructed to clarify the relations between classes of one-parameter, product and flag Ap weights. The main tool for our approach is the weighted Littlewood-Paley- Stein theory associated with the flag structure.

Original languageEnglish
Pages (from-to)545-598
Number of pages54
JournalPacific Journal of Mathematics
Volume302
Issue number2
DOIs
StatePublished - 2019

Keywords

  • Calderón-Zygmund decomposition
  • Duality
  • Interpolation
  • Singular integrals with flag kernels
  • Weighted flag Carleson measure spaces
  • Weighted flag Hardy spaces

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