26 citations · 28 across the 8 of their papers we have counts for
5 papers · 1 filter
The measures with an associated square function operator bounded in
Benjamin Jaye, Fedor Nazarov, Xavier Tolsa
In this paper we provide an extension of a theorem of David and Semmes ('91) to general non-atomic measures. The result provides a geometric characterization of the non-atomic meas…
Singular integrals unsuitable for the curvature method whose -boundedness still implies rectifiability
Petr Chunaev, Joan Mateu, Xavier Tolsa
The well-known curvature method initiated in works of Melnikov and Verdera is now commonly used to relate the -boundedness of certain singular integral operators to the geo…
Characterization of -rectifiability in terms of Jones' square function: Part II
Jonas Azzam, Xavier Tolsa
We show that a Radon measure in which is absolutely continuous with respect to the -dimensional Hausdorff measure is -rectifiable if the so called Jon…
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 is a Radon measure in satisfying $$\limsup_{r\to 0} \frac{μ(B(x,r))}{r}>0…
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 , with an…