Majorization and domination in the Bergman space
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- by Boris Korenblum and Kendall Richards PDF
- Proc. Amer. Math. Soc. 117 (1993), 153-158 Request permission
Abstract:
Let $f$ and $g$ be functions analytic on the unit disk and let $|| \cdot ||$ denote the Bergman norm. Conditions are identified under which there exists an absolute constant $c$, with $0 < c < 1$, such that the relationship $|g(z)| \leqslant |f(z)|(c \leqslant |z| < 1)$ will imply $||g|| \leqslant ||f||$.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
- Alexander Borichev, Håkan Hedenmalm, and Kehe Zhu (eds.), Bergman spaces and related topics in complex analysis, Contemporary Mathematics, vol. 404, American Mathematical Society, Providence, RI; Bar-Ilan University, Ramat Gan, 2006. MR 2246245, DOI 10.1090/conm/404
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 153-158
- MSC: Primary 30C80; Secondary 46E20
- DOI: https://doi.org/10.1090/S0002-9939-1993-1113643-3
- MathSciNet review: 1113643