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-Ríos for singular integrals and maximal operators when p=1.
Brandon Sweeting
NSF MPS-Ascend Postdoctoral Research Fellow, Mathematics
My current research interests are in harmonic analysis, specifically weighted norm inequalities for singular integral operators and Riesz potentials in both the scalar and matrix setting.