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Weighted weak-type inequalities for maximal operators and singular integrals

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arxiv 2311.00828 v1 pith:75Y3VJNV submitted 2023-11-01 math.CA

David Cruz-Uribe , Brandon Sweeting This is my paper · ORCID
classification math.CA
keywords operatorsmaximalintegralssingularweak-typecruz-uribeestimatesfractional
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abstract

We prove quantitative, one-weight, weak-type estimates for maximal operators, singular integrals, fractional maximal operators and fractional integral operators. We consider a kind of weak-type inequality that was first studied by Muckenhoupt and Wheeden and later by Cruz-Uribe, Martell and Perez. We obtain quantitative estimates for these operators in both the scalar and matrix weighted setting using sparse domination techniques. Our results extend those obtained by Cruz-Uribe, Isralowitz, Moen, Pott, and Rivera-R\'ios for singular integrals and maximal operators when $p=1$.

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  1. Off-diagonal matrix extrapolation for Muckenhoupt bases

    math.CA 2025-04 conditional novelty 7.0 of 10

    The authors prove off-diagonal and general-basis Rubio de Francia extrapolation for matrix weights, and show multiparameter bases satisfy the required maximal operator bound.

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