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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Majorization and domination in the Bergman space

Authors: Boris Korenblum and Kendall Richards
Journal: Proc. Amer. Math. Soc. 117 (1993), 153-158
MSC: Primary 30C80; Secondary 46E20
MathSciNet review: 1113643
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Abstract: Let $ f$ and $ g$ be functions analytic on the unit disk and let $ \vert\vert \cdot \vert\vert$ denote the Bergman norm. Conditions are identified under which there exists an absolute constant $ c$, with $ 0 < c < 1$, such that the relationship $ \vert g(z)\vert \leqslant \vert f(z)\vert(c \leqslant \vert z\vert < 1)$ will imply $ \vert\vert g\vert\vert \leqslant \vert\vert f\vert\vert$.

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PII: S 0002-9939(1993)1113643-3
Article copyright: © Copyright 1993 American Mathematical Society

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