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Lorentz-Shimogaki and Boyd theorems for weighted Lorentz spaces
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We prove the Lorentz-Shimogaki and Boyd theorems for the spaces $\Lambda^{p}_{u}(w)$. As a consequence, we give the complete characterization of the strong boundedness of $H$ on these spaces in terms of some geometric conditions on the weights $u$ and $w$, whenever $p > 1$. For these values of $p$, we also give the complete solution of the weak-type boundedness of the Hardy-Littlewood operator on $\Lambda^{p}_{u}(w)$.
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AGORA, Elona, et al. Lorentz-Shimogaki and Boyd theorems for weighted Lorentz spaces. Journal of the London Mathematical Society-Second Series. 2013. Vol. 89, num. 2, pags. 321-336. ISSN 0024-6107. [consulted: 18 of June of 2026]. Available at: https://hdl.handle.net/2445/124948