Existence of principal values of some singular integrals on Cantor sets, and Hausdorff dimension

DOI10.2140/PJM.2023.326.285arXiv2306.05015MaRDI QIDQ6187215

Juan Jesús Donaire, Julià Cufí, Pertti Mattila, Joan Verdera

Publication date: 15 January 2024

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2306.05015

zbMATH Keywords

Cantor setHausdorff dimensionmartingaleCauchy singular integralRiesz singular integral

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20)

Cites Work

• Analytic capacity, the Cauchy transform, and non-homogeneous Calderón-Zygmund theory
• Convergence of singular integrals with general measures
• Riesz transforms and harmonic Lip1-capacity in Cantor sets
• Differentiability of functions in the Zygmund class
• The precise representative for the gradient of the Riesz potential of a finite measure

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