Lipschitz Type Spaces and Landau-Bloch Type Theorems for Harmonic Functions
Acta Mathematica Sinica, Chinese Series
We investigate some properties on harmonic functions and solutions to Poisson equations. We will discuss the Lipschitz type spaces on harmonic functions. Secondly, we establish the Schwarz-Pick type lemma for harmonic functions in the unit ball Bn of Rn, and then we apply it to obtain a Landau-Bloch type 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.
Chen, Shao Lin; Mateljević, Miodrag; Ponnusamy, Saminathan; and Wang, Xian Tao, "Lipschitz Type Spaces and Landau-Bloch Type Theorems for Harmonic Functions" (2017). Journal Articles. 2372.