Reference for Cauchy's estimates of mappings in several complex variables

Question

I want to study higher dimensional analogue of Cauchy's estimate for holomorphic mappings $f:\Omega\subseteq \mathbb{C}^n\to \mathbb{C}^m ,$ where $n,m\in{\mathbb{N}}$. I have seen Cauchy's estimate for holomorphic functions $g:\Omega\subseteq \mathbb{C}^n\to \mathbb{C}$(in terms of partial derivatives), I feel that using Cauchy's estimate for components of $f$, we can give bound for det$f(z)$. But I have not studied this formally. Please suggest a reference to study this.