Weighted estimates for positive operators and Doob maximal operators on filtered measure spaces

2017/08/04 by Wei Chen, Chunxiang Zhu, Chen, Wei +5
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Primary 60G46 #Probability (math.PR) #Secondary 60G42

paper · pdf · doi:10.48550/arxiv.1708.02066

openalex publication_date 2017/08/04 · openalex created_date 2017/08/17 · openalex updated_date 2026/07/28

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 Rⁿ due to Lacey, Sawyer and Uriarte-Tuero \citeLaSaUr. 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.

Citations

• Two Weight Inequalities for Discrete Positive Operators
• Weighted Inequalities for Maximal Operators: Linearization, Localization and Factorization

Related

• Positive operators and maximal operators in a filtered measure space
• A Note on the Boundedness of Doob Maximal Operators on a Filtered Measure Space
• On two-weight norm inequalities for positive dyadic operators
• Restricted weak type inequalities for the one-sided Hardy-Littlewood maximal operators in higher dimensions
• Estimates for Bellman functions related to dyadic-like maximal operators on weighted spaces