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,
$54.95$
[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 
, Proc. Amer. Math. Soc. 102 (1988), 137-138. MR 0915731
[DS] Djrbashian, A.E., Shamoian, F.A., Topics in the theory of 
spaces, Teubner-Texte zur Mathematik, 105, BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1988. MR 1021691
[D] Duren, P., The theory of 
-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 
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
- [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 , Proc. Amer. Math. Soc. 102 (1988), 137-138. MR 0915731
- [DS]
- Djrbashian, A.E., Shamoian, F.A., Topics in the theory of spaces, Teubner-Texte zur Mathematik, 105, BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1988. MR 1021691
- [D]
- Duren, P., The theory of -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 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
