Abstract
Abstract
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.
Publisher
Canadian Mathematical Society
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