Indian Institute of Technology Madras 600 036 Chennai, India; Indian Statistical Institute (ISI), Chennai Center CIT Campus, Taramani, 600 113 Chennai, India
In this paper, we discuss some properties on hyperbolic-harmonic functions in the unit ball of ℂn. First, we investigate the relationship between the weighted Lipschitz functions and the hyperbolic-harmonic Bloch spaces. Then we establish the Schwarz–Pick type theorem for hyperbolic-harmonic functions and apply it to prove the existence of Landau-Bloch constant for functions in α-Bloch spaces.
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