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Book Review

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Book Information:

Authors: Haakan Hedenmalm, Boris Korenblum and Kehe Zhu
Title: Theory of Bergman spaces
Additional book information: Springer-Verlag, New York, 2000, ix+286 pp., ISBN 0-387-98791-6, $54.95

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

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  • [ARS2] Aleman, A., Richter, S., Sundberg, C., The majorization function and the index of invariant subspaces in the Bergman spaces, J. Analyse Math., to appear.
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  • [DS] Djrbashian, A.E., Shamoian, F.A., Topics in the theory of $A^p_\alpha$ spaces, Teubner-Texte zur Mathematik, 105, BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1988. MR 91k:46019
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  • [DKSS1] Duren, P., Khavinson, D., Shapiro, H., Sundberg, C., Contractive zero-divisors in Bergman spaces, Pac. J. Math. 157 (1993), 37-56. MR 94c:30048
  • [DKSS2] Duren, P., Khavinson, D., Shapiro, H., Sundberg, C., Invariant subspaces in Bergman spaces and the Biharmonic equation, Mich. Math. J. 41 (1994), 247-259. MR 95e:46030
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  • [H1] Hedenmalm, H., A Factorization Theorem for Square Area-Integrable Analytic Functions, J. Reine Angew. Math. 422 (1991), 45-68.
  • [H2] Hedenmalm, H., An invariant subspace of the Bergman space having the codimension 2 property. J. Reine Angew. Math. 443 (1993), 1-9. MR 94k:30092
  • [HJS] Hedenmalm, H., Jakobsson, S., Shimorin, S., A maximum principle à la Hadamard for biharmonic operators with applications to the Bergman spaces, C.R. Acad. Sci. Paris Sér I Math. 328 (1999), no. 11, 973-978. MR 2000h:31001
  • [HS] Hedenmalm, H., Shimorin, S., Hele-Shaw flow on hyperbolic surfaces, preprint.
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  • [K1] Korenblum, B., An extension of the Nevanlinna theory, Acta Math. 135 (1975), 187-219. MR 54:13081
  • [K2] Korenblum, B., A Beurling-type theorem, Acta Math., 138 (1976), 265-293. MR 56:5894
  • [MR] McCullough, S., Richter, S., Bergman-type reproducing kernels, contractive divisors, and dilations, preprint.
  • [S] Seip, K., On a theorem of Korenblum, Ark. Math. 32 (1994), 237-243. MR 95f:30054
  • [Z] Zhu, K., Operator theory in function spaces, Marcel Dekker, New York, 1990. MR 92c:47031

Review Information:

Reviewer: Stefan Richter
Affiliation: University of Tennessee
Email: Richter@math.utk.edu
Journal: Bull. Amer. Math. Soc. 39 (2002), 121-127
MSC (2000): Primary 30-02, 46E15, 47B38, 30H05
Published electronically: October 12, 2001
Review copyright: © Copyright 2001 American Mathematical Society
American Mathematical Society