Finely holomorphic functions

DOI10.1016/0022-1236(80)90024-5zbMath0459.46038OpenAlexW2018397246MaRDI QIDQ1152076

Terence J. Lyons

Publication date: 1980

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(80)90024-5

zbMATH Keywords

finely harmonic functionsfinely holomorphic functionsArens-Singer and Jensen measuresVitushkin localization operators

Mathematics Subject Classification ID

Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Spaces of measures (46E27) Potentials and capacities on other spaces (31C15) Other generalizations of analytic functions (including abstract-valued functions) (30G30) Generalizations of potential theory (31C99)

Related Items

Finely holomorphic functions and finely harmonic morphisms, The Dirichlet problem for \(p\)-minimizers on finely open sets in metric spaces, Sur les fonctions finement holomorphes, A theorem in fine potential theory and applications to finely holomorphic functions, Asymptotic paths for subsolutions of quasilinear elliptic equations, Three Problems in Function Theory, Finely continuously differentiable functions, Asymptotic maximum principles for subharmonic functions, Finely continuously differentiable functions, Finely locally injective finely harmonic morphisms, Plurisubharmonic and holomorphic functions relative to the plurifine topology, Domains of existence for finely holomorphic functions, Projection estimates for harmonic measure, Finely harmonic morphisms, Brownian path preserving functions and conformal martingales, An application of fine potential theory to prove a Phragmen-Lindelöf theorem, Fine and quasi connectedness in nonlinear potential theory, Weak-star continuous homomorphisms and a decomposition of orthogonal measures, Projection theorems for hitting probabilities and a theorem of Littlewood, On the growth of subharmonic functions along paths, Tight uniform algebras and algebras of analytic functions

Cites Work

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• Conformal martingales
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• Potentiel fin et algèbres de fonctions. III
• Simplicial cones in potential theory. II: Approximation theorems
• Asymptotic paths for subharmonic functions
• Analytic capacity and rational approximation
• Finely harmonic mappings and finely holomorphic mappings