Quasiadditivity and measure property of capacity and the tangential boundary behavior of harmonic functions

DOI10.1090/S0002-9947-96-01554-1zbMath0856.31004OpenAlexW1860476902MaRDI QIDQ4889949

Hiroaki Aikawa, Alexander Borichev

Publication date: 11 August 1996

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-96-01554-1

zbMATH Keywords

classical capacities\(L^ p\)-capacitiesboundary thin setenergy capacitiestangential boundary behavior of harmonic functions

Mathematics Subject Classification ID

Boundary behavior of harmonic functions in higher dimensions (31B25) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items (12)

Liouville property, Wiener's test and unavoidable sets for hunt processes ⋮ Unavoidable collections of balls for isotropic Lévy processes ⋮ Capacitary estimates of solutions of semilinear parabolic equations ⋮ Unavoidable sets and harmonic measures living on small sets ⋮ On Lundh's percolation diffusion ⋮ Champagne subdomains with unavoidable bubbles ⋮ Quasiadditivity of variational capacity ⋮ Boundary behavior of superharmonic functions satisfying nonlinear inequalities in uniform domains ⋮ Unavoidable collections of balls for censored stable processes ⋮ Capacitary representation of positive solutions of semilinear parabolic equations ⋮ Champagne subregions of the unit disc ⋮ Interpolating sequences for Besov spaces

Cites Work

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• Tangential boundary behavior of functions in Dirichlet-type spaces
• On certain maximal functions and approach regions
• Comparison of L^P- capacity and hausdorff measure
• Quasiadditivity of Riesz capacity.
• Thin Sets at the Boundary
• A Theory of Capacities for Potentials of Functions in Lebesgue Classes.

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