Weighted endpoint estimates for singular integral operators associated with zygmund dilations

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

*Corresponding author for this work

    Research output: Contribution to journalArticle

    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
    Publication statusPublished - Apr 2019

    Keywords

    • Calderón-Zygmund decomposition
    • interpolation
    • multi-parameter singular integral operators
    • weighted Hardy spaces
    • Zygmund dilations

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