Taiwanese Journal of Mathematics

Weighted Endpoint Estimates for Singular Integral Operators Associated with Zygmund Dilations

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

Full-text: Open access

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 $H^p_{\mathfrak{z},w}$ and prove the boundedness for these operators on $H^p_{\mathfrak{z},w}$ for certain $p \leq 1$, 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.

Article information

Source
Taiwanese J. Math., Volume 23, Number 2 (2019), 375-408.

Dates
Received: 7 May 2018
Accepted: 3 December 2018
First available in Project Euclid: 21 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1545361216

Digital Object Identifier
doi:10.11650/tjm/181203

Mathematical Reviews number (MathSciNet)
MR3936005

Zentralblatt MATH identifier
07055574

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B30: $H^p$-spaces

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

Citation

Han, Yongsheng; Li, Ji; Lin, Chin-Cheng; Tan, Chaoqiang; Wu, Xinfeng. Weighted Endpoint Estimates for Singular Integral Operators Associated with Zygmund Dilations. Taiwanese J. Math. 23 (2019), no. 2, 375--408. doi:10.11650/tjm/181203. https://projecteuclid.org/euclid.twjm/1545361216


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