Publications and preprints
Published
Published · Proc. Amer. Math. Soc.
On those weights satisfying a weak-type inequality for the maximal operator
Proceedings of the American Mathematical Society, 2026.
Muckenhoupt and Wheeden introduced a weighted weak (p,p) inequality in which the weight acts as a multiplier rather than as a measure, and derived necessary conditions on the weights for which it holds. This paper shows those conditions are also sufficient for the maximal operator when p > 1, resolving their problem, and proves analogous results for fractional maximal operators.
Published · J. Geom. Anal.
Weighted weak-type bounds for multilinear singular integrals
The Journal of Geometric Analysis, 2026.
We prove multilinear analogs of sharp weighted weak-type bounds for singular integrals, in both the change of measure and multiplier settings. The arguments use only sparse form domination, so the results apply to multilinear Calderón–Zygmund operators and beyond.
Published · Rev. Mat. Complut.
Weighted weak-type inequalities for maximal operators and singular integrals
Revista Matemática Complutense, 2024.
We prove quantitative multiplier weak-type estimates for maximal operators, singular integrals, fractional maximal operators, and fractional integral operators, in both the scalar and matrix weighted settings. Using sparse domination, we extend results of Cruz-Uribe, Isralowitz, Moen, Pott, and Rivera-Ríos from p = 1 to p > 1.
Submitted
Submitted · 2026
Weak-type estimates for the Bergman projection on planar domains
We relate the weak-type behavior of the Bergman projection on a simply connected planar domain to its boundary geometry, through a conformal map from the disk. The projection is weak-type (1,1) when the derivative of this map lies in the Bekollé–Bonami class B1, and we give a necessary condition and sharpened sufficient conditions for weak-type (p,p), via mixed-weighted inequalities on the disk and sparse domination.
In preparation
In preparation
Two-weight multiplier weak-type inequalities for maximal operators and singular integrals
In preparation
On the T(b) theorem in spaces of homogeneous type
In preparation
A T(b) theorem for singular integral operators in the Dunkl setting
In preparation
Sharp dyadic estimates for A2 weights via non-infinitesimal Bellman majorants
We obtain sharp estimates for a family of Carleson sequences related to dyadic A2 weights. Unlike the typical Bellman function argument, the functions here have no infinitesimal extremal splits and do not arise as solutions of a PDE.