Distortion theorem and de la Vallée Poussin means for a class of quasi-convex mappings

Abstract

In this paper, we establish distortion theorems of the Frechet derivative and the Jacobi determinant for the subclass of biholomorphic mappings in several complex variables, which is another extension to higher dimensions of the normalized convex functions on the unit disc $\mathbb{U}$ in $\mathbb{C}$. Meanwhile, the de la Vallee Poussin means for convex functions on $\mathbb{U}$ can be extended to this class of mappings on the Euclidean unit ball. The results presented here would generalize some classical results in one complex variable.