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arXiv · 2506.04025

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

Istvan Berkes·Eduard Stefanescu·Robert Tichy
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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 $x \le \psi(x) \le x^2$.

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Istvan Berkes, Eduard Stefanescu, Robert Tichy. 2025-06-04. A Marcinkiewicz-Zygmund inequality and the Kadec Pe{\l}czyn\'ski theorem in Orlicz spaces. https://arxiv.org/abs/2506.04025

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