Sharp pointwise estimate of α-harmonic functions

2024/02/25 by David Kalaj, Kalaj, David
Mathematics · #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2402.16062

openalex publication_date 2024/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let α>-1 and assume that f is α-harmonic mapping defined in the unit disk that belongs to the Hardy class h^p with p≥ 1. We obtain some sharp estimates of the type |f(z)|≤ g(|r|) ‖f^∗‖_p and |Df(z)|≤ h(|r|)‖f^∗‖_p. We also prove a Schwarz type lemma for the class of α-harmonic mappings of the unit disk onto itself fixing the origin.

Related

• Several properties of α-harmonic functions in the unit disk
• H^p-Norm estimates of the partial derivatives and Schwarz lemma for α-harmonic functions
• Optimal estimates for the gradient of harmonic functions in the unit disk
• Schwarz-Pick type lemma and Landau type theorem for α-harmonic mappings
• Landau type theorem for α-harmonic mappings