The fractional Riesz transform and an exponential potential

DOI10.1090/S1061-0022-2013-01272-6zbMath1281.42011arXiv1204.2135MaRDI QIDQ2856439

B. Jaye, F. L. Nazarov, Alexander Volberg

Publication date: 29 October 2013

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.2135

zbMATH Keywords

nonlinear capacityRiesz transformWolff potentialCalderón-Zygmund capacitytotally lower irregular measure

Mathematics Subject Classification ID

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

Related Items (6)

Wasserstein distance and the rectifiability of doubling measures. I ⋮ On the Maximum Principle for the Riesz Transform ⋮ Reflectionless measures for Calderón-Zygmund operators. II: Wolff potentials and rectifiability ⋮ 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 ⋮ Riesz transforms of non-integer homogeneity on uniformly disconnected sets

Cites Work

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• $L^2$-norm and estimates from below for Riesz transforms on Cantor sets
• A quantitative version of the Besicovitch projection theorem via multiscale analysis
• The boundedness of Riesz 𝑠-transforms of measures in ℝⁿ
• The Capacity Associated to Signed Riesz Kernels, and Wolff Potentials
• Rectifiable Measures in R ⁿ and Existence of Principal Values for Singular Integrals
• Singular Operators with Antisymmetric Kernels, Related Capacities, and Wolff Potentials

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