Weak-type weights and normable Lorentz spaces

Carro, María; del Amo, Alejandro; Soria, Javier

doi:10.1090/S0002-9939-96-03214-5

Weak-type weights and normable Lorentz spaces
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by María J. Carro, Alejandro García del Amo and Javier Soria PDF

Proc. Amer. Math. Soc. 124 (1996), 849-857 Request permission

Abstract:

We show that the Lorentz space $\Lambda ^1(w)$ 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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