Riesz transforms and harmonic Lip1-capacity in Cantor sets

DOI10.1112/S0024611504014790zbMath1089.42009MaRDI QIDQ4664125

Joan Mateu, Xavier Tolsa

Publication date: 5 April 2005

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Cantor setRiesz transformLipschitz harmonic capacity

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25)

Related Items (13)

Principal values for Riesz transforms and rectifiability ⋮ Existence of principal values of some singular integrals on Cantor sets, and Hausdorff dimension ⋮ Calderón-Zygmund capacities and Wolff potentials on Cantor sets ⋮ Principal values for the signed Riesz kernels of non-integer dimension ⋮ Cauchy independent measures and almost-additivity of analytic capacity ⋮ Measures that define a compact Cauchy transform ⋮ Unboundedness of potential dependent Riesz transforms for totally irregular measures ⋮ 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 ⋮ Characterization and semiadditivity of the $\mathcal C^1$-harmonic capacity ⋮ Riesz transforms of non-integer homogeneity on uniformly disconnected sets ⋮ The \(s\)-Riesz transform of an \(s\)-dimensional measure in \(\mathbb R^2\) is unbounded for \(1<s<2\) ⋮ On the semiadditivity of the capacities associated with signed vector valued Riesz kernels

This page was built for publication: Riesz transforms and harmonic Lip1-capacity in Cantor sets