This is an announcement for the paper “Embeddings of Orlicz-Lorentz spaces into $L_1$” by Joscha Prochnohttps://arxiv.org/search/math?searchtype=author&query=Prochno%2C+J.
Abstract: In this article, we show that Orlicz-Lorentz spaces $\ell^n_{M,a}$, $n\in\mathbb N$ with Orlicz function $M$ and weight sequence $a$ are uniformly isomorphic to subspaces of $L_1$ if the norm $|\cdot|_{M,a}$ satisfies certain Hardy-type inequalities. This includes the embedding of some Lorentz spaces $d^n(a,p)$. Our approach is based on combinatorial averaging techniques and we prove a new result of independent interest that relates suitable averages with Orlicz-Lorentz norms.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1902.05043