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# On classes $Q_p^\#$ for Hyperbolic Riemann surfaces

Published:2015-07-13
Printed: Mar 2016
Department of Mathematics, University of Eastern Finland, P.O. Box 111, FIN-80101, Joensuu, Finland
• Huaihui Chen,
Department of Mathematics, Nanjing Normal University, Nanjing 210097, P.R.China
 Format: LaTeX MathJax PDF

## Abstract

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: $Q_p^\#$ class, hyperbolic Riemann surface, spherical Dirichlet function
 MSC Classifications: 30D50 - Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part30F35 - Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]

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