Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590190 | Journal of Functional Analysis | 2015 | 15 Pages |
Abstract
In this paper we study composition operators, CÏ, acting on the Hardy spaces that have symbol, Ï, a universal covering map of the disk onto a finitely connected domain of the form D0\{p1,â¦,pn}, where D0 is simply connected and pi, i=1,â¦,n, are distinct points in the interior of D0. We consider, in particular, conditions that determine compactness of such operators and demonstrate a link with the Poincare series of the uniformizing Fuchsian group. We show that CÏ is compact if, and only if Ï does not have a finite angular derivative at any point of the unit circle, thereby extending the result for univalent and finitely multivalent Ï.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Matthew M. Jones,