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July, 2020 Two-weighted estimates for positive operators and Doob maximal operators on filtered measure spaces
Wei CHEN, Chunxiang ZHU, Yahui ZUO, Yong JIAO
J. Math. Soc. Japan 72(3): 795-817 (July, 2020). DOI: 10.2969/jmsj/80058005

Abstract

We characterize strong type and weak type inequalities with two weights for positive operators on filtered measure spaces. These estimates are probabilistic analogues of two-weight inequalities for positive operators associated to the dyadic cubes in $\mathbb R^n$ due to Lacey, Sawyer and Uriarte-Tuero [30]. Several mixed bounds for the Doob maximal operator on filtered measure spaces are also obtained. In fact, Hytönen–Pérez type and Lerner–Moen type norm estimates for Doob maximal operator are established. Our approaches are mainly based on the construction of principal sets.

Funding Statement

The research of the first author is supported by the National Natural Science Foundation of China (11971419, 11771379), the Natural Science Foundation of Jiangsu Province (BK20161326), and the Jiangsu Government Scholarship for Overseas Studies (JS-2017-228). The research of the fourth author is supported by the National Natural Science Foundation of China (Grant No. 11471337).

Citation

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Wei CHEN. Chunxiang ZHU. Yahui ZUO. Yong JIAO. "Two-weighted estimates for positive operators and Doob maximal operators on filtered measure spaces." J. Math. Soc. Japan 72 (3) 795 - 817, July, 2020. https://doi.org/10.2969/jmsj/80058005

Information

Received: 6 March 2018; Revised: 14 January 2019; Published: July, 2020
First available in Project Euclid: 16 December 2019

zbMATH: 07257211
MathSciNet: MR4125846
Digital Object Identifier: 10.2969/jmsj/80058005

Subjects:
Primary: 60G46
Secondary: 60G42

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 3 • July, 2020
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