$L^2$-norm and estimates from below for Riesz transforms on Cantor sets

DOI10.1512/iumj.2011.60.4304zbMath1259.42010arXiv1012.0941OpenAlexW2964066455MaRDI QIDQ3165247

Vladimir Eiderman, Alexander Volberg

Publication date: 26 October 2012

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.0941

zbMATH Keywords

singular integralCantor setRiesz transformanalytic capacity

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Fractals (28A80) Capacity and harmonic measure in the complex plane (30C85) Hausdorff and packing measures (28A78) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items (5)

Reflectionless measures for Calderón-Zygmund operators. II: Wolff potentials and rectifiability ⋮ The Riesz Transform of Codimension Smaller Than One and the Wolff Energy ⋮ 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 \(1<s<2\) ⋮ The fractional Riesz transform and an exponential potential

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