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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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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?)

[ARS1]
Aleman, A., Richter, S., Sundberg, C., Beurling's theorem for the Bergman space, Acta Math. 177 (1996), 275-310. MR 1440934
[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.
[BK]
Brown, L., Korenblum, B., Cyclic vectors in $A^{-\infty}$, Proc. Amer. Math. Soc. 102 (1988), 137-138. MR 0915731
[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 1021691
[D]
Duren, P., The theory of $H ^{p} $-spaces, Academic Press, New York, 1970. MR 0268655
[DKSS1]
Duren, P., Khavinson, D., Shapiro, H., Sundberg, C., Contractive zero-divisors in Bergman spaces, Pac. J. Math. 157 (1993), 37-56. MR 1197044
[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 1278431
[G]
Garnett, J., Bounded analytic functions, Academic Press, New York, 1981. MR 0628971
[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 1241125
[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 1696190
[HS]
Hedenmalm, H., Shimorin, S., Hele-Shaw flow on hyperbolic surfaces, preprint.
[K]
Koosis, P., Introduction to $H _{p}$ Spaces, Cambridge University Press, 1980, 1998. MR 0565451
[K1]
Korenblum, B., An extension of the Nevanlinna theory, Acta Math. 135 (1975), 187-219. MR 0425124
[K2]
Korenblum, B., A Beurling-type theorem, Acta Math., 138 (1976), 265-293. MR 0447584
[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 1277927
[Z]
Zhu, K., Operator theory in function spaces, Marcel Dekker, New York, 1990. MR 1074007

Review Information:

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