vix.ing · top · new · best · stats · spec

Optimal estimates for harmonic functions in the unit ball

2011/02/19 by David Kalaj, Kalaj, David, Marijan Marković +2
Mathematics · #31A05 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Holomorphic and Operator Theory #math.AP #msc:31A05

paper · pdf · doi:10.48550/arxiv.1102.3995

9 pages

arxiv created 2011/02/19 · openalex publication_date 2011/02/19 · arxiv updated 2011/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find the sharp constants Cp and the sharp functions Cp=Cp(x) in the inequality |u(x)|≤ \fracCp(1-|x|2)(n-1)/p‖u‖hp(Bn), u∈ hp(Bn), x∈ Bn, in terms of Gauss hypergeometric and Euler functions. This extends and improves some results of Axler, Bourdon and Ramey (\citeABR), where they obtained similar results which are sharp only in the cases p=2 and p=1.

Related