Some versions of Khintchine inequality in rearrangement invariant spaces

Abstract:

The main result we will discuss is the following: the square function inequality holds in an rearrangement invariant space X for all sequences of independent mean zero random variables from X if and only if X has the Kruglov property. The same condition is necessary and sufficient for a version of the well-known Maurey's inequality for vector-valued Rademacher series with independent coefficients to hold in X.