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# Inclusion Relations for New Function Spaces on Riemann Surfaces

Published:2012-03-25
Printed: Sep 2013
University of Eastern Finland, Department of Physics and Mathematics, 80101 Joensuu, Finland
• Jouni Rättyä,
University of Eastern Finland, Department of Physics and Mathematics, 80101 Joensuu, Finland
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## Abstract

We introduce and study some new function spaces on Riemann surfaces. For certain parameter values these spaces coincide with the classical Dirichlet space, BMOA or the recently defined $Q_p$ space. We establish inclusion relations that generalize earlier known inclusions between the above-mentioned spaces.
 Keywords: Bloch space, BMOA, $Q_p$, Green's function, hyperbolic Riemann surface
 MSC Classifications: 30F35 - Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx] 30H25 - Besov spaces and $Q_p$-spaces 30H30 - Bloch spaces