Factorable continuity of random fields, with quantitative estimation

We study in this paper the sufficient conditions for enhanced continuity of random fields, i.e. such that the modulus of its continuity allows the factorable representation by the product of random variable on the deterministic module of continuity. We estimate also the ordinary and (possible) exponential moments of these random variables. We consider also the case of random fields with heavy tails of distribution and the so-called rectangle its continuity.