Abstract: Bohr’s type inequalities are studied in this paper: if f is a holomorphic mapping from the unit ball Bⁿ to Bⁿ, f(0)=p, then we have sum from ... and φ_P∈Aut(Bⁿ) such that φ_p=0. As corollaries of the above estimate, we obtain some sharp Bohr’s type modulus inequalities. In particular, when n=1 and |P|→1, then our theorem reduces to a classical result of Bohr. 

Key words: Bohr's inequality, holomorphic mapping, homogeneous expansions