Application of a Riesz-type formula to weighted Bergman spaces

Author:
Ali Abkar

Journal:
Proc. Amer. Math. Soc. **131** (2003), 155-164

MSC (2000):
Primary 31A30; Secondary 30E10, 30H05, 46E10

DOI:
https://doi.org/10.1090/S0002-9939-02-06491-2

Published electronically:
May 13, 2002

MathSciNet review:
1929035

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the unit disk in the complex plane. We consider a class of superbiharmonic weight functions whose growth are subject to the condition for some constant . We first establish a Reisz-type representation formula for , and then use this formula to prove that the polynomials are dense in the weighted Bergman space with weight .

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Additional Information

**Ali Abkar**

Affiliation:
Department of Mathematics, Imam Khomeini International University, P.O. Box 288, Qazvin 34194, Iran

Address at time of publication:
Department of Mathematics, Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-1795, Tehran, Iran

Email:
abkar@ipm.ir

DOI:
https://doi.org/10.1090/S0002-9939-02-06491-2

Received by editor(s):
August 16, 2001

Published electronically:
May 13, 2002

Additional Notes:
This research was supported in part by a grant from the Institute for Theoretical Physics and Mathematics (IPM), Tehran, Iran.

Communicated by:
Juha M. Heinonen

Article copyright:
© Copyright 2002
American Mathematical Society