A Marcinkiewicz-Zygmund inequality and the Kadec Pełczynśki theorem in Orlicz spaces

Abstract

In this paper, we extend the Marcinkiewicz--Zygmund inequality to the setting of Orlicz and Lorentz spaces. Furthermore, we generalize a Kadec--Pełczyński-type result -- originally established by the first and third authors for $L^p$ spaces with $1\le p<2$ -- to a broader class of Orlicz spaces defined via Young functions $\psi$ satisfying $x\le \psi (x)\le x^2$.