Generalization and refinement of Khintchin's inequality

We derive the exponential as well as power decreasing tail estimations for normed sums of centered independent identical distributed (or not) random variables on the Khintchine's form. We consider arbitrary, in particular, non-Rademacher's variables and not only Lebesgue-Riesz rearrangement invariant norms for the random variables. We intend to calculate the value of correspondent limit.