### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 3539-3547 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 141 |

Issue number | 10 |

DOIs | |

State | Published - Aug 1 2013 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Keywords

- Independent random variables
- Quasi-normed symmetric sequence space
- Rearrangement invariant space
- Rosenthal's inequality

## Fingerprint Dive into the research topics of 'A probabilistic version of Rosenthal's inequality'. Together they form a unique fingerprint.

## Cite this

Astashkin, S. V., & Tikhomirov, K. E. (2013). A probabilistic version of Rosenthal's inequality.

*Proceedings of the American Mathematical Society*,*141*(10), 3539-3547. https://doi.org/10.1090/S0002-9939-2013-11713-2