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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Refining the constant in a maximum principle for the Bergman space
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by Chunjie Wang PDF
Proc. Amer. Math. Soc. 132 (2004), 853-855 Request permission

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 $|f(z)|\leq |g(z)|$ ($f,g\in A^2(\mathbb {D})$) in the annulus $c<|z|<1$, then $\|f\|\leq \|g\|$. 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
  • 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
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 853-855
  • MSC (2000): Primary 30C80, 30H05
  • DOI: https://doi.org/10.1090/S0002-9939-03-07137-5
  • MathSciNet review: 2019965