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Weighted estimates for product singular integral operators in Journé’s class on RD-spaces

  • Taotao Zheng ORCID logo EMAIL logo , Yanmei Xiao und Xiangxing Tao
Veröffentlicht/Copyright: 18. April 2024

Abstract

An RD-space 𝑀 is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in 𝑀. In this paper, firstly, the authors give the Plancherel–Pôlya characterization of product weighted Triebel–Lizorkin spaces and product weighted Besov spaces on RD-spaces and make some estimates for the product singular integral operators in Journé’s class on these function spaces. As a result of these conclusions, they present some sufficient conditions for the boundedness of product singular integral operators on the product Lipschitz spaces and product weighted Hardy spaces. Secondly, by the boundedness of lifting and projection operators, they also obtain that the dual spaces of the product weighted Hardy spaces are product weighted Carleson measure spaces. Using the idea of dual, the authors obtain the weighted boundedness of singular integral operators on the product weighted Carleson measure spaces.

MSC 2020: 42B20; 42B25; 46E35

Award Identifier / Grant number: 12326307

Award Identifier / Grant number: 12326308

Award Identifier / Grant number: 12271483

Award Identifier / Grant number: LQ17A010002

Funding statement: This research was funded by National Natural Science Foundation of China (grant numbers 12326307, 12326308, 12271483) and Natural Science Foundation of Zhejiang Province (grant number LQ17A010002).

  1. Communicated by: Christopher D. Sogge

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Received: 2023-07-29
Revised: 2024-03-16
Published Online: 2024-04-18
Published in Print: 2025-02-01

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