Treffer: Application of a Riesz-type formula to weighted Bergman spaces

Title:
Application of a Riesz-type formula to weighted Bergman spaces
Authors:
Ali Abkar
Source:
Proceedings of the American Mathematical Society. 131:155-164
Publisher Information:
American Mathematical Society (AMS), 2002.
Publication Year:
2002
Subject Terms:
Riesz-type representation formula, super-biharmonic weight functions, Spaces of bounded analytic functions of one complex variable, Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions, Topological linear spaces of continuous, differentiable or analytic functions, 0101 mathematics, Approximation in the complex plane, biharmonic Green function, 01 natural sciences
Document Type:
Fachzeitschrift Article<br />Other literature type
File Description:
application/xml
Language:
English
ISSN:
1088-6826
0002-9939
DOI:
10.1090/s0002-9939-02-06491-2
Access URL:
https://www.ams.org/proc/2003-131-01/S0002-9939-02-06491-2/S0002-9939-02-06491-2.pdf
https://www.ams.org/journals/proc/2003-131-01/S0002-9939-02-06491-2/home.html
https://www.jstor.org/stable/1194236
Accession Number:
edsair.doi.dedup.....87a80c23a836ef6721de39adf95fe7ec
Database:
OpenAIRE

Weitere Informationen

Summary: Let \(\mathbb{D}\) denote the unit disk in the complex plane. We consider a class of super\-biharmonic weight functions \(w: \mathbb{D} \to \mathbb{R}^+\) whose growth are subject to the condition \(0\leq w(z)\leq C(1-| z|)\) for some constant \(C\). We first establish a Riesz-type representation formula for \(w\), and then use this formula to prove that the polynomials are dense in the weighted Bergman space with weight \(w\).