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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$.

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

  • [1] B. Korenblum, A maximum principle for the Bergman space, Publ. Mat. 35 (1991), 479-486. MR 1201570 (93j:30018)
  • [2] -, Transformations of zero sets by contractive operators in the Bergman space, Bull. Sci. Math. (2) 114 (1990), 385-394. MR 1077267 (92a:30049)
  • [3] B. Korenblum, R. O'Neil, K. Richards, and K. Zhu, Totally monotone functions with applications to the Bergman space, Trans. Amer. Math. Soc. (to appear). MR 2246245 (2007b:30003)

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