Lipschitz type spaces and Landau-Bloch type theorems for harmonic functions and Poisson equations

2014/07/27 by S-H Chen, Chen, Sh., Saminathan Ponnusamy +4
Mathematics · #31C05 #31C25 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1407.7179

openalex publication_date 2014/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate some properties on harmonic functions and solutions to Poisson equations. First, we will discuss the Lipschitz type spaces on harmonic functions. Secondly, we establish the Schwarz-Pick lemma for harmonic functions in the unit ball \IBⁿ of \IRⁿ, and then we apply it to obtain a Bloch theorem for harmonic functions in Hardy spaces. At last, we use a normal family argument to extend the Landau-Bloch type theorem to functions which are solutions to Poisson equations.

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