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Weighted inequalities for a maximal function on the real line

Published online by Cambridge University Press:  11 July 2007

A. L. Bernardis  and
F. J. Martín-Reyes
A. L. Bernardis
Affiliation:
PEMA-INTEC, Güemes 3450, (3000) Santa Fe, Argentina (bernard@alpha.arcride.edu.ar)
F. J. Martín-Reyes
Affiliation:
Dpto. de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain (martin@anamat.cie.uma.es)
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Abstract

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We consider the maximal operator defined on the real line by which is related to the Cesàro convergence of the singular integrals. We characterize the weights w for which Mα is of weak type, strong type and restricted weak type (p, p) with respect to the measure w(x) dx.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 2 , April 2001 , pp. 267 - 277
Copyright
Copyright © Royal Society of Edinburgh 2001