Application of a Riesz-type formula to weighted Bergman spaces

DOI10.1090/S0002-9939-02-06491-2zbMath1037.31002OpenAlexW1527762268MaRDI QIDQ3151191

Ali Abkar

Publication date: 7 October 2002

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-02-06491-2

zbMATH Keywords

biharmonic Green functionRiesz-type representation formulasuper-biharmonic weight functions

Mathematics Subject Classification ID

Spaces of bounded analytic functions of one complex variable (30H05) Approximation in the complex plane (30E10) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

Related Items

Mean approximation in Bergman spaces of polyanalytic functions, Density of polynomials in certain weighted Dirichlet type spaces, Mean approximation by dilatations in Bergman spaces on the upper half-plane, Non-radial weights and polynomial approximation in spaces of analytic functions, Commutant of multiplication operators in weighted Bergman spaces on polydisk, On the integral representation of superbiharmonic functions, Weighted Bergman spaces induced by rapidly incresing weights, Approximation in weighted analytic Besov spaces and in generalized Fock spaces

Cites Work

• Linear and complex analysis problem book 3. Part 1
• A computation of Green functions for the weighted biharmonic operators \(\Delta| z| ^{-2\alpha}\Delta\), with \(\alpha > -1\)
• Beurling's theorem for the Bergman space
• On the completeness of systems of analytic functions
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