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On Harnack inequality and harmonic Schwarz lemma
- Part of
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- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 10 May 2024, pp. 1-15
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- Article
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In this paper, we study the
$(s, C(s))$-Harnack inequality in a domain 
$G\subset \mathbb {R}^n$ for 
$s\in (0,1)$ and 
$C(s)\geq 1$ 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 
$K\geq 1$. Finally, we provide a type of harmonic Schwarz lemma and improve the Schwarz–Pick estimate for a real-valued harmonic function.
