SHARP DISTORTION THEOREMS FOR A CLASS OF BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES

In this paper,we first establish the sharp growth theorem and the distortion theorem of the Frechet derivative for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in C^(n) with some restricted conditions.We next give the distortion theorem of the Jacobi determinant for biholomorphic mappings defined on the unit ball of C^(n) with an arbitrary norm and the unit polydisk in C^(n) under certain restricted assumptions.Finally we obtain the sharp Goluzin type distortion theorem for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in C^(n) with some additional conditions.The results derived all reduce to the corresponding classical results in one complex variable,and include some known results from the prior literature.