Metric dimensions, generalized integrations, Cauchy transform, and Riemann boundary-value problem on nonrectifiable arcs

DOI10.1007/s10958-013-1175-2zbMath1288.30034OpenAlexW2137143930MaRDI QIDQ357259

Boris A. Kats

Publication date: 30 July 2013

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-013-1175-2

zbMATH Keywords

Cauchy transformsfractional dimensionRiemann boundary value problemsnon-rectifiable arc

Mathematics Subject Classification ID

Boundary value problems in the complex plane (30E25)

Cites Work

• On solvability of the jump problem
• Problèmes de Dirichlet, Neumann, Calderón dans les quasidisques pour les classes höldériennes. (Dirichlet, Neumann and Calderon problems for Hölder classes on quasidiscs)
• The Gauss-Green theorem for fractal boundaries
• Integration over a fractal curve and the jump problem
• A Riemann-Hilbert problem for biorthogonal polynomials
• A weak type inequality for Cauchy transforms of finite measures
• The refined metric dimension with applications
• Bilipschitz maps, analytic capacity, and the Cauchy integral
• Existence and Weak-Type Inequalities for Cauchy Integrals of General Measures on Rectifiable Curves and Sets
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