A Marcinkiewicz-Zygmund inequality and the Kadec Pe{\l}czyn\'ski theorem in Orlicz spaces

TL;DR

This paper extends classical inequalities and theorems from $L^p$ spaces to more general Orlicz spaces, broadening their applicability in functional analysis.

Contribution

It generalizes the Marcinkiewicz--Zygmund inequality and a Kadec--Pe{2}czy
44ski-type result to Orlicz spaces defined by specific Young functions.

Findings

Marcinkiewicz--Zygmund inequality extended to Orlicz and Lorentz spaces

Kadec--Pe{2}czy
44ski theorem generalized to a broader class of Orlicz spaces

Results applicable to spaces with Young functions satisfying $x \,\le\, \psi(x) \,\le\, x^2$

Abstract

In this paper, we extend the Marcinkiewicz--Zygmund inequality to the setting of Orlicz and Lorentz spaces. Furthermore, we generalize a Kadec--Pe{\l}czy\'nski-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 $x \le \psi(x) \le x^2$.