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On Korenblum's maximum principle

Author: Wilhelm Schwick
Journal: Proc. Amer. Math. Soc. 125 (1997), 2581-2587
MSC (1991): Primary 30C80, 30H05
MathSciNet review: 1307563
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Abstract: If $f$ and $g$ are analytic functions in the unit disk and $\|\cdot \|$ is the Bergman norm, conditions are studied under which there exists an absolute constant $c$ such that $|f(z)|\ge |g(z)|$ for $c\le |z|<1$ implies $\|f\|\ge \|g\|$.

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

  • 1. B. Korenblum, A maximum principle for the Bergman space, Publ. Mat. 35 (1991), 479-486. MR 93j:30018
  • 2. -, Transformation of zero sets by contractive operator in the Bergman space, Bull. Sci. Math. (2) 114 (1990), 385-394. MR 92a:30049
  • 3. B. Korenblum and K. Richards, Majorization and domination in the Bergman space, Proc. Amer. Math. Soc. 117 (1993), 153-158. MR 93c:30035
  • 4. G. Polya and G. Szeg\H{o}, Aufgaben und Lehrsätze aus der Analysis I, Springer-Verlag, Berlin, Heidelberg, and New York, 70. MR 42:6160

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Additional Information

Wilhelm Schwick
Affiliation: Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund 50, Germany

Received by editor(s): February 16, 1994
Received by editor(s) in revised form: December 1, 1994
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society