2023/12/27 by Zhenghua Xu, Ting Yu, Xu, Zhenghua +3
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2312.16404
openalex publication_date 2023/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, it is proven that positive harmonic functions defined in the unit disc or the upper half-plane in ℂ are contractions in hyperbolic metrics \citeMarkovic. Furthermore, the same result does not hold in higher dimensions as shown by given counterexamples \citeMelentijevic-P. In this paper, we shall show that positive (or bounded) harmonic functions defined in the unit ball in ℝn are Lipschitz in hyperbolic metrics. The involved method in main results allows to establish essential improvements of Schwarz type inequalities for monogenic functions in Clifford analysis \citeZhang14,Zhang16 and octonionic analysis \citeWang-Bian-Liu in a unified approach.