Type, cotype and generalized Rademacher functions

The main goal of this paper is to show that the traditional Rademacher functions can be replaced, up to a change of constants, by the generalized Rademacher functions in the definitions of type and cotype in complex Banach spaces. It is also shown that there are standard type Kahane inequalities for the generalized Rademacher functions. As an application we prove the continuity of the tensor product of certain multilinear mappings and homogeneous polynomials.