65 citations · 398 across the 74 of their papers we have counts for
91 papers
Failure of almost monotonicity of harmonic measure density ratios at points of vanishing codimension-one density
Luis Lloret, Xavier Tolsa
In this paper we study the behavior of the density ratios of harmonic measure at points with vanishing density. Given an arbitrary open set with harmonic…
Interactions between quantitative rectifiability, singular integrals, and boundary value problems for harmonic functions
Xavier Tolsa
This paper surveys different topics where the theory of quantitative rectifiability plays a central role. First, it reviews the characterization of rectifiability in terms of squar…
New criteria for the rectifiability of Radon measures in terms of Riesz transforms
Xavier Tolsa
In this paper we explore the connection between quantitative rectifiability of measures and the boundedness of the codimension one Riesz transform. Among other things, we pro…
Riesz transforms and the BAUPP and BWGL criteria for uniform rectifiability
Xavier Tolsa
In this note it is shown that if is an -Ahlfors regular measure in such that the -dimensional Riesz transform is bounded in and the so-called B…
Quantitative Carleson's conjecture for Ahlfors regular domains
Emily Casey, Xavier Tolsa, Michele Villa
In this article, we prove a quantitative version of Carleson's conjecture in higher dimension: we characterise those Ahlfors-David regular domains in $\mathbb{R}^{n…
Solvability of the Neumann problem for elliptic equations in chord-arc domains with very big pieces of good superdomains
Mihalis Mourgoglou, Xavier Tolsa
Let be a bounded chord-arc domain, let be an elliptic operator in associated with a matrix having Dini mean osci…