Decoupling inequalities and some mean-value theorems

The purpose of this paper is to present some further applications of the general decoupling theory from B-D] and B-D2] to certain diophantine issues. In particular, we consider mean value estimates relevant to the Bombieri- Iwaniec approach to exponential sums and arising in the work of Robert and Sargos R-S]. Our main input is a new mean-value theorem.