Convergence of singular integrals with general measures

DOI10.4171/JEMS/149zbMath1163.42005arXiv0711.1291OpenAlexW1999681880MaRDI QIDQ1012479

Joan Verdera, Pertti Mattila

Publication date: 21 April 2009

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.1291

zbMATH Keywords

martingalessingular integralsprincipal values

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20)

Related Items (15)

The Huovinen transform and rectifiability of measures ⋮ Reflectionless measures for Calderón-Zygmund operators. I: General theory ⋮ The precise representative for the gradient of the Riesz potential of a finite measure ⋮ Existence of principal values of some singular integrals on Cantor sets, and Hausdorff dimension ⋮ Principal values for the signed Riesz kernels of non-integer dimension ⋮ Mass transport and uniform rectifiability ⋮ Reflectionless measures for Calderón-Zygmund operators. II: Wolff potentials and rectifiability ⋮ Measures that define a compact Cauchy transform ⋮ Estimates for the maximal singular integral in terms of the singular integral: the case of even kernels ⋮ On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1 ⋮ The Riesz Transform of Codimension Smaller Than One and the Wolff Energy ⋮ Small local action of singular integrals on spaces of non-homogeneous type ⋮ \(L^2\)-boundedness of gradients of single-layer potentials and uniform rectifiability ⋮ Gradient of the single layer potential and quantitative rectifiability for general Radon measures ⋮ Reflectionless Measures and the Mattila-Melnikov-Verdera Uniform Rectifiability Theorem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Singular integrals on Sierpinski gaskets
• Wavelets and singular integrals on curves and surfaces
• Analytic capacity, rectifiability, Menger curvature and the Cauchy integral
• The fall of the doubling condition in Calderón-Zygmund theory
• Painlevé's problem and the semiadditivity of analytic capacity.
• On geometric properties of harmonic \(\text{Lip}_ 1\)-capacity
• The Cauchy integral, analytic capacity, and uniform rectifiability
• Principal values for Riesz transforms and rectifiability
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• Des intégrales singulières bornées sur un ensemble de Cantor
• A nicely behaved singular integral on a purely unrectifiable set
• Cotlar's inequality without the doubling condition and existence of principal values for the Cauchy integral of measures
• Rectifiable Measures in R ⁿ and Existence of Principal Values for Singular Integrals
• Principal values for the Cauchy integral and rectifiability

This page was built for publication: Convergence of singular integrals with general measures