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On Korenblum's maximum principle

Author(s): Wilhelm Schwick
Journal: Proc. Amer. Math. Soc. 125 (1997), 2581-2587.
MSC (1991): Primary 30C80, 30H05
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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:

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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