| Convergence of Composition Operators on Hardy-Smirnov Space |
| Received:November 20, 2009 Revised:January 13, 2011 |
| Key Words:
composition operators convergence Hardy-Smirnov space.
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| Fund Project:Supported by the Natural Science Foundation of Yunnan Province (Grant No.2009ZC013X) and Basic Research Foundation of Education Bureau of Yunnan Province (Grant No.09Y0079). |
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| Abstract: |
| We consider the convergence of composition operators on Hardy-Smirnov space over a simply connected domain properly contained in the complex plane. The convergence of the power of a composition operator is also considered. Our approach is a method from Joel H. Shapiro and Wayne Smith's celebrated work (Journal of Functional Analysis 205 (2003) 62-89). The resulting space is usually not the one obtained from the classical Hardy space of the unit disc by conformal mapping. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.04.021 |
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