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April, 2019 Weighted Endpoint Estimates for Singular Integral Operators Associated with Zygmund Dilations
Yongsheng Han, Ji Li, Chin-Cheng Lin, Chaoqiang Tan, Xinfeng Wu
Taiwanese J. Math. 23(2): 375-408 (April, 2019). DOI: 10.11650/tjm/181203

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.

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Yongsheng Han. Ji Li. Chin-Cheng Lin. Chaoqiang Tan. Xinfeng Wu. "Weighted Endpoint Estimates for Singular Integral Operators Associated with Zygmund Dilations." Taiwanese J. Math. 23 (2) 375 - 408, April, 2019. https://doi.org/10.11650/tjm/181203

Information

Received: 7 May 2018; Accepted: 3 December 2018; Published: April, 2019
First available in Project Euclid: 21 December 2018

zbMATH: 07055574
MathSciNet: MR3936005
Digital Object Identifier: 10.11650/tjm/181203

Subjects:
Primary: 42B20 , 42B30

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

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

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Vol.23 • No. 2 • April, 2019
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