Large deviations of Gaussian measures on spaces l(p) and L-p, p>=2

Now the theory of summing of independent random elements with values in Banach space is developing extensively. In view of the central limit theorem Gaussian distributions arise as limiting. In the paper the exact asymptotics for large deviations of Gaussian measures of sets on general Banach spaces are found. The main result obtained in the paper is applied for calculation of asymptotics of Gaussian measures of balls on the spaces iota(p) and L-p, p greater than or equal to 2 (in the case of the Wiener measure). Applications to the theory of statistics of type omega(p), p greater than or equal to 2, are discussed.