On Classes for Hyperbolic Riemann Surfaces

Aulaskari, Rauno ; Chen, Huaihui

Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 13-29

Résumé

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.

Détail

DOI : 10.4153/CMB-2015-033-8

Mots-clés : 30D45, 30D50, 30F35, Q# p class, hyperbolic Riemann surface, spherical Dirichlet function

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