On Harnack inequality and harmonic Schwarz lemma

: Kargar, Rahim

Publisher: Cambridge University Press

: Cambridge

: 2024

: Canadian Mathematical Bulletin

: 67

: 4

: 940

: 954

: 0008-4395

: 1496-4287

DOI: https://doi.org/10.4153/S0008439524000298

: https://doi.org/10.4153/S0008439524000298

: https://research.utu.fi/converis/portal/detail/Publication/421363386

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.

on-harnack-inequality-and-harmonic-schwarz-lemma.pdf