The aim of this paper is twofold. First, we adapt the Burgeth’s spherical cap method [Manuscripta Math. 77:283–291, 1992 by Burgeth and Proceedings of the NATO Advanced Research Workshop on Classical and Modem Potential Theory and Applications, pp 133–147, 1994 by Burgeth] to the planar case to establish some Schwarz type lemmas for mappings admitting general Poisson type representations on the unit disk. Second, we prove a Landau type theorem for \(T_\alpha \)-harmonic functions introduced by Olofsson (J Anal Math 123:227–249, 2014).

本文的目的是双重的。首先，我们采用 Burgeth 的球冠方法 [Manuscripta Math. 77:283–291, 1992 by Burgeth and Proceedings of the NATO Advanced Research Workshop on Classical and Modem Potential Theory and Applications, pp 133–147, 1994 by Burges] 到平面案例建立一些 Schwarz 型引理用于映射承认泊松将军单元盘上的类型表示。其次，我们证明了Olofsson (J Anal Math 123:227–249, 2014) 引入的\(T_\alpha \) -谐波函数的朗道型定理。