|
Composition operators on weighted Dirichlet spaces
Author(s):
Nina
Zorboska
Journal:
Proc. Amer. Math. Soc.
126
(1998),
2013-2023.
MSC (1991):
Primary 47B38;
Secondary 30H05
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We characterize bounded and compact composition operators on weighted Dirichlet spaces. The method involves integral averages of the determining function for the operator, and the connection between composition operators on Dirichlet spaces and Toeplitz operators on Bergman spaces. We also present several examples and counter-examples that point out the borderlines of the result and its connections to other themes.
References:
- 1.
- C.C.Cowen and B.D.MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, 1995. CMP 96:14
- 2.
- D.H.Luecking, Inequalities on Bergman spaces, Illinois J.Math. 25 (1981), 1-11. MR 82e:30072
- 3.
- D.H.Luecking, Trace ideal criteria for Toeplitz operators, J. Functional Analysis 73 (1987), 345-368. MR 88m:47046
- 4.
- D.H.Luecking and K.Zhu, Composition operators belonging to the Schatten ideals, American J.Math. 114 (1992), 1127-1145. MR 93i:47032
- 5.
- B.D. MacCluer and J.H. Shapiro, Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canadian J.Math. 38 (1986), 878-906. MR 87h:47048
- 6.
- D.J. Newman, H.S. Shapiro, Embedding theorems for weighted classes of harmonic and analytic functions, Michigan Math. J. 9 (1962), 249-255
- 7.
- V.L.Oleinik, Embedding theorems for weighted classes of harmonic and analytic functions, Journal of Soviet Mathematics 9 (1978), 228-243.
- 8.
- J.H. Shapiro, Compact composition operators on spaces of boundary regular holomorphic functions, Proc.Amer.Math.Soc 100 (1987), 49-57. MR 88c:47059
- 9.
- J.H. Shapiro, The essential norm of a composition operator, Annals Math. 125 (1987), 375-404. MR 88c:47058
- 10.
- J.H. Shapiro, Composition Operators and Classical Function Theory, Springer-Verlag, New York, 1993. MR 94k:47049
- 11.
- J.H. Shapiro, Private communication
- 12.
- W. Smith and D.A. Stegenga, A geometric characterization of Holder domains, J.London Math.Soc (2) 35, (1987), 471-480. MR 88f:30011
- 13.
- N. Zorboska, Composition operators with closed range, Trans. Amer. Math. Soc. 344 (1994), 791-801. MR 94k:47050
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
47B38,
30H05
Retrieve articles in all Journals with MSC
(1991):
47B38,
30H05
Additional Information:
Nina
Zorboska
Affiliation:
Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
Email:
zorbosk@ccu.umanitoba.ca
DOI:
10.1090/S0002-9939-98-04266-X
PII:
S 0002-9939(98)04266-X
Keywords:
Composition operators,
Dirichlet spaces,
Carleson measures,
angular derivatives.
Received by editor(s):
March 13, 1996
Received by editor(s) in revised form:
December 10, 1996
Additional Notes:
The author was supported in part by an NSERC grant.
Communicated by:
Theodore W. Gamelin
Copyright of article:
Copyright
1998,
American Mathematical Society
|
Comments: webmaster@ams.org