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.
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Rahim Kargar (2024) studied this question.
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