Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Surjective isometries of weighted Bergman spaces


Author: Clinton J. Kolaski
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $ \vert g\vert$.


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

  • [1] C. Horowitz, Zeros of functions in the Bergman spaces, Duke Math. J. 41 (1974), 693-710. MR 0357747 (50:10215)
  • [2] C. Kolaski, Isometries of Bergman spaces over bounded Runge domains, Canad. J. Math. 33 (1981), 1157-1164. MR 638372 (83b:32028)
  • [3] -, Isometries of Weighted Bergman spaces, Canad. J. Math. 34 No. 4 (1982), 910-915. MR 672684 (84a:46054)
  • [4] D. H. Luecking, Representation and duality in weighted spaces of analytic functions, Indiana Univ. Math. J. 34, No. 2 (1985), 319-336. MR 783918 (86e:46020)
  • [5] W. Rudin, Function theory in the unit ball of $ {{\mathbf{C}}^n}$, Springer-Verlag, New York, 1980. MR 601594 (82i:32002)
  • [6] A. Selberg, Automorphic functions and integral operators, Seminars on Analytic Functions, II, Institute for Advanced Study, Princeton, N.J., 1957, pp. 152-161.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46E15, 30H05, 32F05, 32H10, 46J15

Retrieve articles in all journals with MSC: 46E15, 30H05, 32F05, 32H10, 46J15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0953008-7
Keywords: Bergman space, isometry, automorphism
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society