Weak-type weights and normable Lorentz spaces

We show that the Lorentz space Λ1(w)\Lambda ^1(w) is a Banach space if and only if the Hardy-Littlewood maximal operator MM 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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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1996, Vol.124 (3), p.849-857
Main Authors: Carro, María J., del Amo, Alejandro García, Soria, Javier
Format: Article
Language:English
Subjects:
Anàlisi de Fourier
Banach space
Decreasing functions
Espais funcionals
Fourier analysis in several variables
Funcions de diverses variables
Interpolation
Linear function spaces and their duals
Mathematical functions
Mathematical inequalities
Mathematical theorems
Research article
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Description
Summary:We show that the Lorentz space Λ1(w)\Lambda ^1(w) is a Banach space if and only if the Hardy-Littlewood maximal operator MM 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.
ISSN:0002-9939
1088-6826
1088-6826
DOI:10.1090/S0002-9939-96-03214-5