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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 | References | Similar Articles | Additional Information

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 $c<0.69472.$

References [Enhancements On Off] (What's this?)

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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

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

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