We prove some probabilistic relations between sums of independent random variables and the corresponding disjoint sums, which strengthen the well-known Rosenthal inequality and its generalizations. As a consequence we extend the inequalities proved earlier by Montgomery-Smith and Junge for rearrangement invariant spaces to the quasi-normed case.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Independent random variables
- Quasi-normed symmetric sequence space
- Rearrangement invariant space
- Rosenthal's inequality