Geodesic
On Disjointly Homogeneous Orlicz--Lorentz Spaces
Matematičeskie zametki, Tome 108 (2020) no. 5, pp. 643-656

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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.
Keywords: Orlicz–Lorentz space, Orlicz space, Orlicz function, symmetric space, disjointly homogeneous space, weakly compact set, Matuszewska–Orlicz indices. 
@article{MZM_2020_108_5_a0,
     author = {S. V. Astashkin and S. I. Strakhov},
     title = {On {Disjointly} {Homogeneous} {Orlicz--Lorentz} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--656},
     publisher = {mathdoc},
     volume = {108},
     number = {5},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_108_5_a0/}
}
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S. V. Astashkin; S. I. Strakhov. On Disjointly Homogeneous Orlicz--Lorentz Spaces. Matematičeskie zametki, Tome 108 (2020) no. 5, pp. 643-656. http://geodesic.mathdoc.fr/item/MZM_2020_108_5_a0/