Composition operators acting on holomorphic Sobolev spaces
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- by Boo Rim Choe, Hyungwoon Koo and Wayne Smith PDF
- Trans. Amer. Math. Soc. 355 (2003), 2829-2855 Request permission
Abstract:
We study the action of composition operators on Sobolev spaces of analytic functions having fractional derivatives in some weighted Bergman space or Hardy space on the unit disk. Criteria for when such operators are bounded or compact are given. In particular, we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces. Sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal.References
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Additional Information
- Boo Rim Choe
- Affiliation: Department of Mathematics, Korea University, Seoul 136–701, Korea
- MR Author ID: 251281
- Email: choebr@math.korea.ac.kr
- Hyungwoon Koo
- Affiliation: Department of Mathematics, Korea University, Seoul 136–701, Korea
- MR Author ID: 606733
- Email: koohw@math.korea.ac.kr
- Wayne Smith
- Affiliation: Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822
- MR Author ID: 213832
- Email: wayne@math.hawaii.edu
- Received by editor(s): April 4, 2002
- Received by editor(s) in revised form: August 6, 2002
- Published electronically: March 14, 2003
- Additional Notes: The second author’s research was partially supported by KRF2001-041-D00012
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 2829-2855
- MSC (2000): Primary 47B33; Secondary 30D55, 46E15
- DOI: https://doi.org/10.1090/S0002-9947-03-03273-2
- MathSciNet review: 1975402