Weighted endpoint estimates for singular integral operators associated with zygmund dilations

Yongsheng Han, Ji Li, Chin Cheng Lin, Chaoqiang Tan, Xinfeng Wu

Research output: Contribution to journalArticlepeer-review

Abstract

The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. We develop the theory of the weighted multi-parameter Hardy space H z,w p and prove the boundedness for these operators on H z,w p for certain p ≤ 1, which provide endpoint estimates for those singular integral operators studied by Ricci-Stein [31] and Fefferman-Pipher [15]. We also establish the Calderón-Zygmund decomposition and interpolation theorem in this setting.

Original languageEnglish
Pages (from-to)375-408
Number of pages34
JournalTaiwanese Journal of Mathematics
Volume23
Issue number2
DOIs
StatePublished - Apr 2019

Keywords

  • Calderón-Zygmund decomposition
  • Interpolation
  • Multi-parameter singular integral operators
  • Weighted Hardy spaces
  • Zygmund dilations

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