Norm approximation by polynomials in some weighted Bergman spaces

DOI10.1006/JFAN.2001.3851zbMath1059.30049OpenAlexW1999016178MaRDI QIDQ1614774

Ali Abkar

Publication date: 8 September 2002

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

Full work available at URL: https://doi.org/10.1006/jfan.2001.3851

zbMATH Keywords

weight functionbiharmonic Green functionsuperbiharmonic functionBergman space, Hardy spaceharmonic compensator

Mathematics Subject Classification ID

Spaces of bounded analytic functions of one complex variable (30H05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

Related Items (9)

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 ⋮ An expansive multiplier property for operator-valued Bergman inner functions

Cites Work

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• Linear and complex analysis problem book 3. Part 2
• 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
• A Factoring Theorem for The Bergman Space
• On the completeness of systems of analytic functions

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