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Weighted Lorentz norm inequalities for general maximal operators associated with certain families of Borel measures

Published online by Cambridge University Press:  14 November 2011

María Dolores Sarrión Gavilán
María Dolores Sarrión Gavilán
Affiliation:
Departamento de Economía Aplicada (Estadística y Econometría), Facultad de Ciencias Económicas y Empresariales, Universidad de Málaga, 29013 Málaga, Spain
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Abstract

Given a certain family ℱ of positive Borel measures and γ ∈ [0, 1), we define a general onesided maximal operator and we study weighted inequalities in Lp,q spaces for these operators. Our results contain, as particular cases, the characterisation of weighted Lorentz norm inequalities for some well-known one-sided maximal operators such as the one-sided Hardy–Littlewood maximal operator associated with a general measure , the one-sided fractional maximal operator and the maximal operator associated with the Cesèro-α averages.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 2 , 1998 , pp. 403 - 424
Copyright
Copyright © Royal Society of Edinburgh 1998

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