On Local Behavior of Holomorphic Functions Along Complex Submanifolds of C^N

In this paper we establish some general results on local behavior of holomorphic functions along complex submanifolds of ${\text{Co}}^N$. As a corollary, we present multi-dimensional generalizations of an important result of Coman and Poletsky on Bernstein type inequalities on transcendental curves in ${\text{Co}}^2$.