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Weak-type weights and normable Lorentz spaces

Authors: María J. Carro, Alejandro García del Amo and Javier Soria
Journal: Proc. Amer. Math. Soc. 124 (1996), 849-857
MSC (1991): Primary 42B25, 46E30
MathSciNet review: 1307501
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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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Additional Information

María J. Carro
Affiliation: Departamento Matemàtica Aplicada i Anàlisi, Universidad de Barcelona, 08071 Barcelona, Spain

Alejandro García del Amo
Affiliation: Departamento Análisis Matemático, Facultad de Ciencias, Matemáticas, Universidad Complutense, 28040 Madrid, Spain
Address at time of publication: Departamento Matemática Pura y Aplicada, Facultad de Ciencias, Universidad de Salamanca, 37008 Salamanca, Spain

Javier Soria
Affiliation: Departamento Matemàtica Aplicada i Anàlisi, Universidad de Barcelona, 08071 Barcelona, Spain

Received by editor(s): September 14, 1994
Additional Notes: The first and third authors were partially supported by DGICYT PB94–0879. \endgraf The second author was partially supported by DGICYT PB94–0243.
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society