2020/04/13 by Jiaolong Chen, David Kalaj, Chen, Jiaolong +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2004.06211
openalex publication_date 2020/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Assume that p∈[1,∞] and u=Ph[ϕ], where ϕ∈ Lp(\mathbbSn-1,ℝn) and u(0) = 0. Then we obtain the sharp inequality |u(x)|≤ Gp(|x|)‖ϕ‖Lp for some smooth function Gp vanishing at 0. Moreover, we obtain an explicit form of the sharp constant Cp in the inequality ‖Du(0)‖≤ Cp‖ϕ‖Lp. These two results generalize and extend some known result from harmonic mapping theory (\cite[Theorem 2.1]kalaj2018) and hyperbolic harmonic theory (\cite[Theorem 1]bur).