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Inclusion Relations for New Function Spaces on Riemann Surfaces

Open Access article
  Published:2012-03-25
 Printed: Sep 2013
  • Rauno Aulaskari,
    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 Bloch space, BMOA, $Q_p$, Green's function, hyperbolic Riemann surface
MSC Classifications: 30F35, 30H25, 30H30 show english descriptions Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]
Besov spaces and $Q_p$-spaces
Bloch spaces
30F35 - Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]
30H25 - Besov spaces and $Q_p$-spaces
30H30 - Bloch spaces
 

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