X. Tolsa

activity

20002026

most citedUniform rectifiability, Calderon-Zygmund operators with odd kernel, and quasiorthogonality

65 citations · 398 across the 74 of their papers we have counts for

collaborators

Showing 2014 · math.CAShow all

5 papers · 2 filters

math.CA2014

Square functions of fractional homogeneity and Wolff potentials

Vasileios Chousionis, Laura Prat, Xavier Tolsa

In this paper it is shown that for anymeasure $μ$ in $R^{d}$ and for a non-integer $0 < s < d$ , the Wolff energy $\displaystyle{\iint_0^\infty(\frac{μ(B(x,r))}{r^s})^2\,\frac{dr…

math.CA2014

Rectifiable measures, square functions involving densities, and the Cauchy transform

Xavier Tolsa

This paper is devoted to the proof of two related results. The first one asserts that if $μ$ is a Radon measure in $R^{d}$ satisfying $$\limsup_{r\to 0} \frac{μ(B(x,r))}{r}>0…

math.CA2014★ 26 cited

A T(P) theorem for Sobolev spaces on domains

Martí Prats, Xavier Tolsa

Recently, V. Cruz, J. Mateu and J. Orobitg have proved a T(1) theorem for the Beurling transform in the complex plane. It asserts that given $0 < s \leq 1$ , $1 < p < \infty$ with $s p > 2$ an…

math.CA2014

Rectifiability via a square function and Preiss' theorem

Xavier Tolsa, Tatiana Toro

Let $E$ be a set in $R^{d}$ with finite $n$ -dimensional Hausdorff measure $H^{n}$ such that $lim inf_{r \to 0} r^{- n} H^{n} (B (x, r) \cap E) > 0$ for $H^{n}$ -a.e. $x \in E$ . In this paper i…

math.CA2014★ 2 cited

Square functions and uniform rectifiability

Vasilis Chousionis, John Garnett, Triet Le +1

In this paper it is shown that an Ahlfors-David $n$ -dimensional measure $μ$ on $R^{d}$ is uniformly $n$ -rectifiable if and only if for any ball $B (x_{0}, R)$ centered at $\oper…