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

摘要

In this paper, we investigate some properties on harmonic functions andsolutions to Poisson equations. First, we will discuss the Lipschitz typespaces on harmonic functions. Secondly, we establish the Schwarz-Pick lemma forharmonic functions in the unit ball $\IB^n$ of $\IR^n$, and then we apply it toobtain a Bloch theorem for harmonic functions in Hardy spaces. At last, we usea normal family argument to extend the Landau-Bloch type theorem to functionswhich are solutions to Poisson equations.