Agora, ElonaAntezana, JorgeCarro Rossell, María JesúsSoria de Diego, F. Javier2018-10-012018-10-012013-10-150024-6107https://hdl.handle.net/2445/124948We 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 $\Lambda^{p}_{u}(w)$.16 p.application/pdfeng(c) London Mathematical Society, 2013Desigualtats (Matemàtica)Anàlisi harmònicaInequalities (Mathematics)Harmonic analysisinfo:eu-repo/semantics/article6275542018-10-01info:eu-repo/semantics/openAccess