Comparison of weak and strong moments for vectors with independent   coordinates
  We show that for $p\ge 1$, the $p$-th moment of suprema of linear combinations of independent centered random variables are comparable with the sum of the first moment and the weak $p$-th moment provided that $2q$-th and $q$-th integral moments of these variables are comparable for all $ q \ge 2$. The latest condition turns out to be necessary in the i.i.d. case. 
Rafa{\l} Lata{\l}a, Marta Strzelecka
math.PR math.MG