On harmonic functions and the hyperbolic metric
classification
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functionshalf--planeharmonichyperbolicpositiveamercontractionsdefined
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Motivated by some recent results of Kalaj and Vuorinen (Proc. Amer. Math. Soc., 2012), we prove that positive harmonic functions defined in the upper half--plane are contractions w.r.t. hyperbolic metrics of half--plane and positive part of the real line, respectively
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