English

Weighted weak-type inequalities for maximal operators and singular integrals

Classical Analysis and ODEs 2023-11-03 v1

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=1p=1.

Keywords

Cite

@article{arxiv.2311.00828,
  title  = {Weighted weak-type inequalities for maximal operators and singular integrals},
  author = {David Cruz-Uribe and Brandon Sweeting},
  journal= {arXiv preprint arXiv:2311.00828},
  year   = {2023}
}
R2 v1 2026-06-28T13:09:03.536Z