On Korenblum’s maximum principle
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- by Wilhelm Schwick PDF
- Proc. Amer. Math. Soc. 125 (1997), 2581-2587 Request permission
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
- Boris Korenblum, A maximum principle for the Bergman space, Publ. Mat. 35 (1991), no. 2, 479–486. MR 1201570, DOI 10.5565/PUBLMAT_{3}5291_{1}2
- Boris Korenblum, Transformation of zero sets by contractive operators in the Bergman space, Bull. Sci. Math. 114 (1990), no. 4, 385–394. MR 1077267
- Boris Korenblum and Kendall Richards, Majorization and domination in the Bergman space, Proc. Amer. Math. Soc. 117 (1993), no. 1, 153–158. MR 1113643, DOI 10.1090/S0002-9939-1993-1113643-3
- Georg Pólya and Gábor Szegő, Aufgaben und Lehrsätze aus der Analysis. Band I: Reihen, Integralrechnung, Funktionentheorie, Heidelberger Taschenbücher, Band 73, Springer-Verlag, Berlin-New York, 1970 (German). Vierte Auflage. MR 0271277
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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2581-2587
- MSC (1991): Primary 30C80, 30H05
- DOI: https://doi.org/10.1090/S0002-9939-97-03247-4
- MathSciNet review: 1307563