|
Composition operators between Bergman and Hardy spaces
Author(s):
Wayne
Smith
Journal:
Trans. Amer. Math. Soc.
348
(1996),
2331-2348.
MSC (1991):
Primary 47B38;
Secondary 30D55, 46E15
MathSciNet review:
1357404
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We study composition operators between weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Particular choices for the weights yield results on composition operators between the classical unweighted Bergman and Hardy spaces.
References:
- [A]
- Ahlfors, L.V., Conformal Invariants, McGraw-Hill, New York, 1973. MR 50:10211
- [D]
- Duren, P.L., Theory of
 Spaces, Academic Press, New York, 1970. MR 42:3552 - [ESS]
- Essén, M., Shea, D.F. and Stanton, C.S., A value-distribution criterion for the class
 , and some related questions, Ann. Inst. Fourier (Grenoble) 35 (1985), 127--150. MR 87e:30041 - [GP]
- Gehring, F. W. and Palka, B. P., Quasiconformally homogeneous domains, J. Analyse Math. 30 (1976), 172--199. MR 55:10676
- [H]
- Hunziker, H., Kompositionsoperatoren auf klassischen Hardyräumen, Thesis, Universität Zurich (1989).
- [HJ]
- Hunziker, H. and Jarchow, H., Composition operators which improve integrability, Math. Nachr. 152 (1991), 83--91. MR 93d:47061
- [L]
- Littlewood, J.E., On inequalities in the theory of functions, Proc. London Math. Soc. 23 (1925), 481--519.
- [MS]
- MacCluer, B.D. and Shapiro, J.H., Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canad. J. Math. 38 (1986), 878--906. MR 87h:47048
- [R]
- Riedl, R., Composition operators and geometric properties of analytic functions, Thesis, Universität Zurich (1994).
- [Sh]
- Shapiro, J.H., The essential norm of a composition operator, Annals of Math. 127 (1987), 375--404. MR 88c:47058
- [Sh2]
- Shapiro, J.H., Composition Operators and Classical Function Theory, Springer-Verlag, New York Berlin, 1993. MR 94k:47049
- [ST]
- Shapiro, J.H. and Taylor, P.D., Compact, nuclear and Hilbert-Schmidt composition operators on
 , Indiana University Math. J. 23 (1973), 471--496. MR 48:4816 - [St]
- Stanton, C. S., Counting functions and majorization for Jensen measures, Pacific J. Math. 125 (1986), 459--468. MR 88c:32002
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (1991):
47B38,
30D55, 46E15
Retrieve articles in all Journals with
MSC (1991):
47B38,
30D55, 46E15
Additional Information:
Wayne
Smith
Affiliation:
Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822
Email:
wayne@math.hawaii.edu
DOI:
10.1090/S0002-9947-96-01647-9
PII:
S 0002-9947(96)01647-9
Keywords:
Bergman spaces,
Hardy spaces,
composition operators,
Nevanlinna counting function
Received by editor(s):
February 23, 1995
Copyright of article:
Copyright
1996,
American Mathematical Society
|
