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On Classes for Hyperbolic Riemann Surfaces

Published online by Cambridge University Press:  20 November 2018

Rauno Aulaskari and
Huaihui Chen
Rauno Aulaskari
Affiliation:
Department of Mathematics, University of Eastern Finland, P.O. Box 111, FIN-80101, Joensuu, Finland e-mail: rauno.aulaskari@uef.fi
Huaihui Chen
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, P.R.China e-mail: hhchen@njnu.edu.cn
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Abstract

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The ${{Q}_{p}}$ spaces of holomorphic functions on the disk, hyperbolic Riemann surfaces or complex unit ball have been studied deeply. Meanwhile, there are a lot of papers devoted to the $Q_{p}^{\#}$ classes of meromorphic functions on the disk or hyperbolic Riemann surfaces. In this paper, we prove the nesting property (inclusion relations) of $Q_{p}^{\#}$ classes on hyperbolic Riemann surfaces. The same property for ${{Q}_{p}}$ spaces was also established systematically and precisely in earlier work by the authors of this paper.

Keywords

30D4530D5030F35Q# p classhyperbolic Riemann surfacespherical Dirichlet function

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 1 , 01 March 2016, pp. 13 - 29
Copyright
Copyright © Canadian Mathematical Society 2016

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