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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Refining the constant in a maximum principle for the Bergman space


Author: Chunjie Wang
Journal: Proc. Amer. Math. Soc. 132 (2004), 853-855
MSC (2000): Primary 30C80, 30H05
Published electronically: September 5, 2003
MathSciNet review: 2019965
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Abstract: Let $A^2(\mathbb{D} )$ be the Bergman space over the open unit disk $\mathbb{D} $ in the complex plane. Korenblum conjectured that there is an absolute constant $c,~0<c<1$, such that whenever $\vert f(z)\vert\leq \vert g(z)\vert$ ( $f,g\in A^2(\mathbb{D} )$) in the annulus $c<\vert z\vert<1$, then $\Vert f\Vert\leq \Vert g\Vert$. In this note we give an example to show that $c<0.69472.$


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Additional Information

Chunjie Wang
Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Address at time of publication: Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300160, People’s Republic of China
Email: wcj498@eyou.com

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07137-5
PII: S 0002-9939(03)07137-5
Received by editor(s): October 28, 2002
Received by editor(s) in revised form: November 12, 2002
Published electronically: September 5, 2003
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society