2024/04/10 by Blaschke, Petr, Engliš, Miroslav, Youssfi, El-Hassan · 1 citation
#32A36 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 31C05 #Secondary 33C55
paper · doi:10.48550/arxiv.2404.07384
We~describe a Dirichlet-type space of H-harmonic functions, i.e. functions annihilated by the hyperbolic Laplacian on~the unit ball of the real n-space, as~the analytic continuation (in~the spirit of Rossi and Vergne) of the corresponding weighted Bergman spaces. Characterizations in terms of derivatives are given, and the associated semi-inner product is shown to be Moebius invariant. We~also give a formula for the corresponding reproducing kernel. Our~results solve an open problem addressed by M.~Stoll in his book ``Harmonic and subharmonic function theory on the hyperbolic ball'' (Cambridge University Press, 2016).