On classes $Q_p^\#$ for Hyperbolic Riemann surfaces
Printed: Mar 2016
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
by the authors of this paper.
$Q_p^\#$ class, hyperbolic Riemann surface, spherical Dirichlet function
30D50 - Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part
30F35 - Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]