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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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On Korenblum’s maximum principle
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by Chunjie Wang PDF
Proc. Amer. Math. Soc. 134 (2006), 2061-2066 Request permission

Abstract:

Let $A^2(\mathbb {D})$ be the Bergman space over the open unit disk $\mathbb {D}$ in the complex plane. Korenblum’s maximum principle states that there is an absolute constant $c\in (0,1)$, such that whenever $|f(z)|\leq |g(z)|$ ($f,g\in A^2(\mathbb {D})$) in the annulus $c<|z|<1$, then $\|f\|_{A^2}\leq \|g\|_{A^2}$. In this paper we prove that Korenblum’s maximum principle holds with $c=0.25018$.
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Additional Information
  • Chunjie Wang
  • Affiliation: Department of Mathematics, Hebei University of Technology, Tianjin 300130, People’s Republic of China
  • Email: wcj498@eyou.com
  • Received by editor(s): December 10, 2004
  • Received by editor(s) in revised form: February 14, 2005
  • Published electronically: January 5, 2006
  • Additional Notes: This work was supported by NNSF of China No. 10401002 and the Doctoral Foundation of Hebei University of Technology.
  • Communicated by: Joseph A. Ball
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 2061-2066
  • MSC (2000): Primary 30C80, 30H05
  • DOI: https://doi.org/10.1090/S0002-9939-06-08311-0
  • MathSciNet review: 2215775