Rearrangement invariant norms of symmetric sequence norms of independent sequences of random variables

LetX ₁,X ₂, …,X _n be a sequence of independent random variables, letM be a rearrangement invariant space on the underlying probability space, and letN be a symmetric sequence space. This paper gives an approximate formula for the quantity ‖‖(X _i )‖ _N ‖ _M wheneverL _q embeds intoM for some 1≤q<∞. This extends work of Johnson and Schechtman who tackled the case whenN=ℓ _p , and recent work of Gordon, Litvak, Schütt and Werner who obtained similar results for Orlicz spaces. The author was partially supported by NSF grant DMS 9870026, and a grant from the Research Office of the University of Missouri.