We prove a very general sharp inequality of the H\"older--Young--type for
functions defined on infinite dimensional Gaussian spaces. We begin by
considering a family of commutative products for functions which interpolates
between the point--wise and Wick products; this family arises naturally in the
context of stochastic differential equations, through Wong--Zakai--type
approximation theorems, and plays a key role in some generalizations of the
Beckner--type Poincar\'e inequality. We then obtain a crucial integral
representation for that family of products which is employed, together with a
generalization of the classic Young inequality due to Lieb, to prove our main
theorem. We stress that our main inequality contains as particular cases the
H\"older inequality and Nelson's hyper-contractive estimate, thus providing a
unified framework for two fundamental results of the Gaussian analysis
