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Book Review

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Book Information

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

References:

[ARS1]
Aleman, A., Richter, S., Sundberg, C., Beurling's theorem for the Bergman space, Acta Math. 177 (1996), 275-310. MR 98a:46034

[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 89e:46025

[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

[D]
Duren, P., The theory of $H ^{p} $-spaces, Academic Press, New York, 1970. MR 42:3552

[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

[G]
Garnett, J., Bounded analytic functions, Academic Press, New York, 1981. MR 83g:30037

[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.

[K]
Koosis, P., Introduction to $H _{p}$ Spaces, Cambridge University Press, 1980, 1998. MR 81c:30062

[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

Additional Information:

Reviewer(s):
Stefan Richter
Affiliation: University of Tennessee
Email: Richter@math.utk.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 39 (2002), 121-127.

MSC (2000): Primary 30-02, 46E15, 47B38, 30H05
DOI: 10.1090/S0273-0979-01-00927-2
PII: S 0273-0979(01)00927-2
Posted: October 12, 2001
Copyright of article: Copyright 2001, American Mathematical Society

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