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Abstract In this paper, we study the (s, C (s) ) -Harnack inequality in a domain G Rⁿ for s (0, 1) and C (s) 1 and present a series of inequalities related to (s, C (s) ) -Harnack functions and the Harnack metric. We also investigate the behavior of the Harnack metric under K -quasiconformal and K -quasiregular mappings, where K 1. Finally, we provide a type of harmonic Schwarz lemma and improve the Schwarz–Pick estimate for a real-valued harmonic function.
Rahim Kargar (Fri,) studied this question.
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