On the semiadditivity of the capacities associated with signed vector valued Riesz kernels

DOI10.1090/S0002-9947-2012-05724-2zbMath1278.42020arXiv1007.2122MaRDI QIDQ2844724

Laura Prat

Publication date: 19 August 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.2122

zbMATH Keywords

capacityRiesz kernel

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15) Capacity theory and generalizations (32U20)

Related Items (8)

Removable singularities for Lipschitz caloric functions in time varying domains ⋮ The precise representative for the gradient of the Riesz potential of a finite measure ⋮ Calderón-Zygmund capacities and Wolff potentials on Cantor sets ⋮ Removable singularities for solutions of the fractional heat equation in time varying domains ⋮ Some Calderón-Zygmund kernels and their relations to Wolff capacities and rectifiability ⋮ Analytic capacity and projections ⋮ The Riesz Transform of Codimension Smaller Than One and the Wolff Energy ⋮ Riesz transforms of non-integer homogeneity on uniformly disconnected sets

Cites Work

• \(C^ m\) approximation by solutions of elliptic equations, and Calderón-Zygmund operators
• Null sets for the capacity associated to Riesz kernels
• Painlevé's problem and the semiadditivity of analytic capacity.
• On geometric properties of harmonic \(\text{Lip}_ 1\)-capacity
• Calderón-Zygmund capacities and Wolff potentials on Cantor sets
• Analytic capacity and measure
• Vector-valued Riesz potentials: Cartan-type estimates and related capacities
• Capacities associated with scalar signed Riesz kernels, and analytic capacity
• Characterization and semiadditivity of the $\mathcal C^1$-harmonic capacity
• The Capacity Associated to Signed Riesz Kernels, and Wolff Potentials
• Riesz transforms and harmonic Lip1-capacity in Cantor sets
• The semiadditivity of continuous analytic capacity and the inner boundary conjecture
• Analytic capacity: discrete approach and curvature of measure
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