Uniformly perfect subsets of the real line and John domains

DOI10.1007/BF03321044zbMath1057.30007MaRDI QIDQ1884438

Vladimir V. Andrievskii

Publication date: 1 November 2004

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

zbMATH Keywords

Green's functionJohn domainlogarithmic capacityuniformly perfect setconformal invariantstarlike domain\(c\)-dense set

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Conformal mappings of special domains (30C20) Approximation by polynomials (41A10) Capacity and harmonic measure in the complex plane (30C85) Inverse theorems in approximation theory (41A27)

Cites Work

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• On the boundary continuity of conformal maps
• Uniformly perfect sets and the Poincaré metric
• Quantitative approximation theorems for elliptic operators
• Approximation of harmonic functions on compact sets in \(\mathbb{C}\)
• Metric properties of harmonic measures
• The Poincaré Metric of Plane Domains
• Injectivity theorems in plane and space
• The Nikol'skii-Timan-Dzjadyk theorem for functions on compact sets of the real line

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