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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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Full text of review: PDF   This review is available free of charge.
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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Aleman, A., Richter, S., Sundberg, C., The majorization function and the index of invariant subspaces in the Bergman spaces, J. Analyse Math., to appear.
Brown, L., Korenblum, B., Cyclic vectors in $A^{-\infty}$, Proc. Amer. Math. Soc. 102 (1988), 137-138. MR 0915731
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 1021691
Duren, P., The theory of $H ^{p} $-spaces, Academic Press, New York, 1970. MR 0268655
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Garnett, J., Bounded analytic functions, Academic Press, New York, 1981. MR 0628971
Hedenmalm, H., A Factorization Theorem for Square Area-Integrable Analytic Functions, J. Reine Angew. Math. 422 (1991), 45-68.
Hedenmalm, H., An invariant subspace of the Bergman space having the codimension 2 property. J. Reine Angew. Math. 443 (1993), 1-9. MR 1241125
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 1696190
Hedenmalm, H., Shimorin, S., Hele-Shaw flow on hyperbolic surfaces, preprint.
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Korenblum, B., A Beurling-type theorem, Acta Math., 138 (1976), 265-293. MR 0447584
McCullough, S., Richter, S., Bergman-type reproducing kernels, contractive divisors, and dilations, preprint.
Seip, K., On a theorem of Korenblum, Ark. Math. 32 (1994), 237-243. MR 1277927
Zhu, K., Operator theory in function spaces, Marcel Dekker, New York, 1990. MR 1074007

Review Information:

Reviewer: Stefan Richter
Affiliation: University of Tennessee
Journal: Bull. Amer. Math. Soc. 39 (2002), 121-127
Published electronically: October 12, 2001
Review copyright: © Copyright 2001 American Mathematical Society