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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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Journal of the London Mathematical Society-Second Series, 2013, vol. 89, num. 2, p. 321-336

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Lorentz-Shimogaki and Boyd theorems for weighted Lorentz spaces