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The one-sided dyadic Hardy—Littlewood maximal operator

Published online by Cambridge University Press:  03 October 2014

María Lorente  and
Francisco J. Martín-Reyes
María Lorente
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciências, Universidad de Málaga, 29071 Málaga, Spain, ([email protected]; [email protected])
Francisco J. Martín-Reyes
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciências, Universidad de Málaga, 29071 Málaga, Spain, ([email protected]; [email protected])
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Abstract

The main aim of this paper is to introduce an appropriate dyadic one-sided maximal operator , smaller than the one-sided Hardy–Littlewood maximal operator M+ but such that it controls M+ in a similar way to how the usual dyadic maximal operator controls the Hardy-Littlewood maximal operator. We characterize the weighted inequalities for this dyadic one-sided maximal operator.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 5 , October 2014 , pp. 991 - 1006
Copyright
Copyright © Royal Society of Edinburgh 2014 

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