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arXiv · 2311.00828

Weighted weak-type inequalities for maximal operators and singular integrals

David Cruz-Uribe·Brandon Sweeting
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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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David Cruz-Uribe, Brandon Sweeting. 2023-11-01. Weighted weak-type inequalities for maximal operators and singular integrals. https://arxiv.org/abs/2311.00828

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