The Schwarz inequalities at the boundary point of the Hartogs triangles

Abstract

The purpose of this paper is twofold. On one hand, we will calculate the explicit form for the Carathéodory-Reiffen pseudometric of the generalized Hartogs triangles in , which is defined by the inequality . On the other hand, we aim to show a version of the boundary Schwarz lemma for holomorphic self-mappings of the generalized Hartogs triangles. In particular, we present an example of the boundary Schwarz lemma for a bounded non-homogeneous pseudoconvex domain with a Levi-flat boundary.