P. Hitczenko et Sj. Montgomerysmith, TANGENT SEQUENCES IN ORLICZ AND REARRANGEMENT-INVARIANT SPACES, Mathematical proceedings of the Cambridge Philosophical Society, 119, 1996, pp. 91-101
Let (f(n)) and (g(n)) be two sequences of random variables adapted to
an increasing sequence of sigma-algebras (F-n) such that the condition
al distributions of f(n) and g(n) given F-n coincide. Suppose further
that the sequence (g(n)) is conditionally independent. Then it is know
n that \\Sigma f(k)\\(p) less than or equal to C\\Sigma g(k)\\(p), 1 l
ess than or equal to p less than or equal to infinity, where the numbe
r C is a universal constant. The aim of this paper is to extend. this
result to certain classes of Orlicz and rearrangement invariant spaces
. This paper includes fairly general techniques for obtaining rearrang
ement invariant inequalities from Orlicz norm inequalities.