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Evaluation operators on the Bergman space†

Published online by Cambridge University Press:  24 October 2008

Kehe Zhu
Kehe Zhu
Affiliation:
Department of Mathematics, State University of New York, Albany, NY 12222, U.S.A. E-mail: kzhu©math.albany.edu
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Extract

Let D be the open unit disc in the complex plane C and let dA be the normalized area measure on D. The Bergman space is the space of analytic functions f in D such that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 3 , May 1995 , pp. 513 - 523
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

REFERENCES

[1]Amar, E.. Suites d'interpolation pour les classes de Bergman de la boule et du polydisque de Cn. Canadian J. Math. 30 (1978), 711–737.CrossRefGoogle Scholar
[2]Berger, C., Coburn, L. and Zhu, K.. Function theory on Cartan domains and the Berezin-Toeplitz functional calculus. Amer. J. Math. 110 (1988), 921–953.CrossRefGoogle Scholar
[3]Coifman, R. and Rochberg, R.. Representation theorems for holomorphic and harmonic functions in L p. Astérisque 77 (1980), 11–66.Google Scholar
[4]Duren, P., Khavinson, D., Shapiro, H. and Sundberg, C.. Contractive zero-divisors in Bergman spaces. Pacific J. Math. 157 (1993), 37–56.Google Scholar
[5]Hedenmalm, H.. A factorization theorem for square area-integrable analytic functions. J. Reine Angew. Math. 422 (1991), 45–68.Google Scholar
[6]Hedenmalm, H.. An invariant subspace of the Bergman space having the codimension two property. J. Reine Angew. Math. 443 (1991), 1–9.Google Scholar
[7]Horowitz, C.. Zeros of functions in the Bergman spaces. Duke Math. J. 41 (1974), 693–710.CrossRefGoogle Scholar
[8]Mcdonald, G. and Sundberg, C.. Toeplitz operators on the disk. Indiana Univ. Math. J. 28 (1979), 595–611.CrossRefGoogle Scholar
[9]Rochberg, R.. Interpolation by functions in Bergman spaces. Michigan Math. J. 28 (1982), 229–237.Google Scholar
[10]Rudin, W.. Functional Analysis, 2nd Edition (McGraw Hill, 1991).Google Scholar
[11]Seip, K.. Beurling type density theorems in the unit disc. Invent. Math. 113 (1994), 21–39.CrossRefGoogle Scholar
[12]Zhu, K.. Operator Theory in Function Spaces (Marcel Dekker, 1990).Google Scholar
[13]Zhu, K.. Interpolating sequences for the Bergman space. Michigan Math. J. 41 (1994), 73–86.CrossRefGoogle Scholar