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.
Original language | English |
---|---|
Pages (from-to) | 2829-2855 |
Number of pages | 27 |
Journal | Transactions of the American Mathematical Society |
Volume | 355 |
Issue number | 7 |
DOIs | |
Publication status | Published - 2003 Jul |
Keywords
- Bergman space
- Composition operator
- Fractional derivative
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics