Normality Criterion Concerning Total Derivatives of Holomorphic Functions in $$ {\mathbb {C}}^n $$

Abstract

This paper continues investigation of conditions involving values shared by holomorphic functions and their total derivatives which imply the normality for a family of holomorphic functions concerning the total derivatives in \( {\mathbb {C}}^n \). Consequently, we obtain normality criterion of a family \( {\mathcal {F}} \) of holomorphic functions f, where each function shares complex values with their linear total differential polynomials \( L_D^k(f) \) in \( {\mathbb {C}}^n \).