2023/12/11 by Miloš Arsenović, Arsenović, Miloš, Jelena Gajić +1
Mathematics · #2010: 30C80 #31A05 #31A10 #35J25 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2312.06894
openalex publication_date 2023/12/11 · openalex created_date 2023/12/15 · openalex updated_date 2026/07/28
We obtain Schwarz-Pick lemma for (α, β)-harmonic functions u in the disc, where α and β are complex parameters satisfying \Re α+ \Re β> -1. We prove sharp estimate of derivative at the origin for such functions in terms of Lp norm of the boundary function. Also, we give asymptotically sharp estimate of the norm of the derivative at point z in the unit disc. These estimates are extended to higher order derivatives. Our results extend earlier results for α-harmonic and Tα-harmonic functions.