From the 1 of 8 linked papers with an AI index.
1 citations · 1 across the 2 of their papers we have counts for
8 papers
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…
Solvability of the Neumann problem for elliptic equations in chord-arc domains with very big pieces of good superdomains
Mihalis Mourgoglou, Xavier Tolsa
The paper proves that for a bounded chord-arc domain with Dini‑oscillating coefficients, if the regularity problem is solvable in some L^q (q>p), the boundary satisfies a weak p‑Po…
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…
The measures with -bounded Riesz transform and the Painlevé problem
Damian DÄ browski, Xavier Tolsa
In this work we provide a geometric characterization of the measures in with polynomial upper growth of degree such that the -dimensional Riesz transf…
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…
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…