Surjective isometries of weighted Bergman spaces
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- by Clinton J. Kolaski PDF
- Proc. Amer. Math. Soc. 105 (1989), 652-657 Request permission
Abstract:
Let $\Omega$ be a bounded, simply connected domain in ${{\mathbf {C}}^n} = {R^{2n}}$, let $F \in {L^1}({m_\Omega })$ be positive and continuo on $\Omega$, and let $B_F^P(\Omega ) = {L^p}(Fdm) \cap H(\Omega )(0 < p < \infty )$ denote the weighted Bergman space over $\Omega$. We characterize those automorphisms $\Phi$ of $\Omega$ such that the map $f \to g \cdot (f \circ \Phi )$ is a surjective isometry of $B_F^P(\Omega )$, including an explicit description of $|g|$.References
- Charles Horowitz, Zeros of functions in the Bergman spaces, Duke Math. J. 41 (1974), 693–710. MR 357747
- Clinton J. Kolaski, Isometries of Bergman spaces over bounded Runge domains, Canadian J. Math. 33 (1981), no. 5, 1157–1164. MR 638372, DOI 10.4153/CJM-1981-087-1
- Clinton J. Kolaski, Isometries of weighted Bergman spaces, Canadian J. Math. 34 (1982), no. 4, 910–915. MR 672684, DOI 10.4153/CJM-1982-063-5
- Daniel H. Luecking, Representation and duality in weighted spaces of analytic functions, Indiana Univ. Math. J. 34 (1985), no. 2, 319–336. MR 783918, DOI 10.1512/iumj.1985.34.34019
- Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594 A. Selberg, Automorphic functions and integral operators, Seminars on Analytic Functions, II, Institute for Advanced Study, Princeton, N.J., 1957, pp. 152-161.
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 652-657
- MSC: Primary 46E15; Secondary 30H05, 32F05, 32H10, 46J15
- DOI: https://doi.org/10.1090/S0002-9939-1989-0953008-7
- MathSciNet review: 953008