Abstract
A characterization of disjointly homogeneous Orlicz–Lorentz function spaces \(\Lambda_{\varphi,w}\) is obtained. It is used to find necessary and sufficient conditions for an analog of the classical Dunford–Pettis theorem about the equi-integrability of weakly compact sets in \(L_1\) to hold in the space \(\Lambda_{\varphi,w}\). It is also shown that there exists an Orlicz function \(\Phi\) with the upper Matuszewska–Orlicz index equal to \(1\) for which such an analog in the space \(\Lambda_{\Phi,w}\) does not hold. This answers a recent question of Leśnik, Maligranda, and Tomaszewski.
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Astashkin, S.V., Strakhov, S.I. On Disjointly Homogeneous Orlicz–Lorentz Spaces. Math Notes 108, 631–642 (2020). https://doi.org/10.1134/S0001434620110012
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DOI: https://doi.org/10.1134/S0001434620110012