Bounds for the Characteristic Functions of the System of Monomials in Random Variables and of Its Trigonometric Analogue

Using a multidimensional analogue of Vinogradov's inequality for a trigonometric integral, the upper bounds are constructed for the moduli of the characteristic functions both of the system of monomials in components of a random vector with an absolutely continuous distribution in and of the systemwhere is uniformly distributed in [0, l]^s.