文摘
In this paper, we generalize a recent work of Liu et al. from the open unit ball \({\mathbb {B}}^n\subset {\mathbb {C}}^n\) to more general bounded strongly pseudoconvex domains with \(C^2\) boundaries. It turns out that part of the main result in this paper is in some certain sense just a part of results in a work of Bracci and Zaitsev. However, the proofs are significantly different: the argument in this paper involves a simple growth estimate for the Carathéodory metric near the boundary of \(C^2\) domains and the well-known Graham’s estimate on the boundary behavior of the Carathéodory metric on strongly pseudoconvex domains, while Bracci and Zaitsev use other arguments.