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Weak-type weights and normable Lorentz spaces
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Abstract
We show that the Lorentz space A1(w) is a Banach space if and
only if the Hardy-Littlewood maximal operator M satisfies a certain weak-type
estimate. We also consider the case of general measures. Finally, we study
some properties of several indices associated to these spaces.
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CARRO ROSSELL, María Jesús, GARCÍA DEL AMO, Alejandro and SORIA DE DIEGO, F. Javier. Weak-type weights and normable Lorentz spaces. Proceedings of the American Mathematical Society. 1996. Vol. 124, num. 3, pags. 849-857. ISSN 1088-6826. [consulted: 9 of June of 2026]. Available at: https://hdl.handle.net/2445/7624