Abstract
In this paper we find conditions for boundedness of self-map composition operators on weighted spaces of holomorphic functions on the upper half-plane for two kinds of weights which are of moderate growth.
Highlights
Different properties of composition operators between weighted spaces of holomorphic functions on the unit disc or upper half-plane have been the subject of many papers in recent decades (Ardalani, 2014; Ardalani & Lusky, 2011, 2012a, 2012b; Bonet, 2003; Bonet, Domanski, & Lindstrom, 1998, 1999; Bonet, Fritz, & Jorda, 2005; Cowen, 1995; Madigan, 1993, Shapiro, 1987; Zhu, 1990)
In Theorem 2.3 of Bonet et al (1998), authors have characterized boundedness of self-map composition operators on weighted spaces of holomorphic functions on the unit disc in terms of associated weight which satisfies well-known growth condition that is used by Lusky (1995)
During 2007–2010, he completed his PhD in Pure Mathematics (Complex and Functional Analysis) and worked as Faculty of computer science, Electrical Engineering and Mathematics, University of Paderborn, Paderborn Germany
Summary
Different properties of composition operators between weighted spaces of holomorphic functions on the unit disc or upper half-plane have been the subject of many papers in recent decades (Ardalani, 2014; Ardalani & Lusky, 2011, 2012a, 2012b; Bonet, 2003; Bonet, Domanski, & Lindstrom, 1998, 1999; Bonet, Fritz, & Jorda, 2005; Cowen, 1995; Madigan, 1993, Shapiro, 1987; Zhu, 1990). In Theorem 2.3 of Bonet et al (1998), authors have characterized boundedness of self-map composition operators on weighted spaces of holomorphic functions on the unit disc in terms of associated weight which satisfies well-known growth condition that is used by Lusky (1995). In this paper we intend to find conditions for boundedness of all self-map composition operators on weighted spaces of holomorphic functions on the upper half-plane for standard weights in the sense of Ardalani (2014), Ardalani and Lusky (2011, 2012a) and for a new type of weights on the upper half-plane which we call it type(II) weights.
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