88 citations · 134 across the 23 of their papers we have counts for
19 papers · 1 filter
Existence of principal values of some singular integrals on Cantor sets, and Hausdorff dimension
J. Cufí, J. J. Donaire, P. Mattila +1
Consider a standard Cantor set in the plane of Hausdorff dimension 1. If the linear density of the associated measure vanishes, then the set of points where the principal value…
Birth and life of the boundedness of the Cauchy Integral on Lipschitz graphs
Joan Verdera
We review various motives for considering the problem of estimating the Cauchy Singular Integral on Lipschitz graphs in the norm. We follow the thread that led to the solut…
The precise representative for the gradient of the Riesz potential of a finite measure
Julià Cufí, Augusto C. Ponce, Joan Verdera
Given a finite nonnegative Borel measure in , we identify the Lebesgue set of the vector-valued function $$V_{s}(x)…
Capacitary differentiability of potentials of finite Radon measures
Joan Verdera
We study differentiability properties of a potential of the type , where is a finite Radon measure in and the kernel satisfies $|\nabla^j K(x)| \le…
About the Jones-Wolff Theorem on the Hausdorff dimension of harmonic measure
Julià Cufí, Xavier Tolsa, Joan Verdera
These are the lecture notes of a seminar held at the Universitat Autònoma de Barcelona where the Jones-Wolff theorem about the dimension of harmonic measure in the plane is explain…
On square functions with independent increments and Sobolev spaces on the line
Julià Cufí, Artur Nicolau, Andreas Seeger +1
We prove a characterization of some -Sobolev spaces involving the quadratic symmetrization of the Calderón commutator kernel, which is related to a square function with differ…
Differentiability properties of Riesz potentials of finite measures and non-doubling Calderón-Zygmund theory
Julià Cufí, Joan Verdera
We study differentiability properties of Riesz potentials of finite Borel measures in dimension d larger than 2. The Riesz kernel has homogeneity 2-d. In dimension 2 we consider lo…
Characterizing regularity of domains via Riesz transforms on their boundaries
D. Mitrea, M. Mitrea, J. Verdera
Given a domain D in R^d with mild geometric measure theoretic assumptions on its boundary, we show that boundedness of the principal value Riesz tranforms (witn kernel of homogenei…
A general form of Green Formula and Cauchy Integral Theorem
Julia Cufi, Joan Verdera
We prove a general form of Green Formula and Cauchy Integral Theorem for arbitrary closed rectifiable curves in the plane.
Boundary regularity of rotating vortex patches
Taoufik Hmidi, Joan Mateu, Joan Verdera
We show that the boundary of a rotating vortex patch (or V-state, in the terminology of Deem and Zabusky) is of class C^infinity provided the patch is close enough to the bifurcati…
The maximal singular integral : estimates in terms of the singular integral
Joan Verdera
This is an expository paper on the characterization of the even (or odd) smooth homogeneous convolution Calderón-Zygmund operators in R^n such that the maximal singular integral ca…
A new characterization of Sobolev spaces on
Roc Alabern, Joan Mateu, Joan Verdera
In this paper we present a new characterization of Sobolev spaces on Euclidian spaces (). Our characterizing condition is obtained via a quadratic multiscale expressi…
Capacities associated with scalar signed Riesz kernels, and analytic capacity
Joan Mateu, Laura Prat, Joan Verdera
The real and imaginari parts of the Cauchy kernel in the plane are scalar Riesz kernels of homogeneity -1. One can associate with each of them a natural notion of capacity related…
New estimates for the maximal singular integral
Joan Mateu, Joan Orobitg, Carlos Perez +1
In this paper we pursue the study of the problem of controlling the maximal singular integral by the singular integral . Here is a smooth homogeneous Calderón-Zygm…
Extra cancellation of even Calderon-Zygmund operators and quasiconformal mappings
Joan Mateu, Joan Orobitg, Joan Verdera
We discuss a special class of Beltrami coefficients whose associated quasiconformal mapping is bilipschitz. These are of the form the characteristic function of a planar bounded do…
Convergence of Singular integrals with general measures
P. Mattila, J. Verdera
We show that L^2-bounded singular integral in metric spaces with respect to general measures and kernels converge weakly. This implies a kind of average convergence almost everywhe…
Estimates for the maximal singular integral in terms of the singular integral:the case of even kernels
Joan Mateu, Joan Orobitg, Joan Verdera
The purpose of this paper is to describe the smooth homogeneous Calderon-Zygmund operators for which the maximal singular integral T*f may be controlled by the singular integral Tf…
Lp and weak L1 estimates for the maximal Riesz transform and the maximal Beurling transform
Joan Mateu, Joan Verdera
We estimate in Lp the maximal Riesz transform in terms of the Riesz transform itself for p greater than 1. In the limiting case p=1 the weak L1 inequality is shown to fail. Surpris…
The capacity associated to signed Riesz kernels, and Wolff potentials
Joan Mateu, Laura Prat, Joan Verdera
There is a natural capacity associated to any vector valued Riesz kernel of a given homogeneity. If we are in the plane and the kernel is the Cauchy kernel, then this capacity is a…