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THE HARDY–LITTLEWOOD MAXIMAL FUNCTION AND WEIGHTED LORENTZ SPACES

Published online by Cambridge University Press:  01 February 1997

MARÍA J. CARRO  and
JAVIER SORIA
MARÍA J. CARRO
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08071 Barcelona, Spain. E-mail: carro@erber.mat.ub.es E-mail: soria@cerber.mat.ub.es
JAVIER SORIA
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08071 Barcelona, Spain. E-mail: carro@erber.mat.ub.es E-mail: soria@cerber.mat.ub.es
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Abstract

We study the boundedness of the Hardy–Littlewood maximal function in weighted Lorentz spaces, using some new techniques on distribution and rearrangement functions. Our goal is to give a unified version of some well-known weighted inequalities in ℝn and ℝ+, showing the relation between the theories.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 55 , Issue 1 , February 1997 , pp. 146 - 158
Copyright
The London Mathematical Society 1997

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