Weighted inequalities for a maximal function on the real line

Authors
Bernardis, AL Martin-Reyes, FJ
Citation
Al. Bernardis et Fj. Martin-reyes, Weighted inequalities for a maximal function on the real line, P RS EDIN A, 131, 2001, pp. 267-277
Citations number
5
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
ISSN journal
03082105 → ACNP
Volume
131
Year of publication
2001
Part
2
Pages
267 - 277
Database
ISI
SICI code
0308-2105(2001)131:<267:WIFAMF>2.0.ZU;2-1
Abstract
We consider the maximal operator defined on the real line by M(alpha)f(x) = sup(R >0) 1/(2R)(1+alpha) f(R < \x-y\< 2R) \f(y)\(\x-y\ - R) (alpha) dy, -1 < alpha <0, which is related to the Cesaro convergence of the singular integrals. We ch aracterize the weights w for which M-alpha is of weak type, strong type and restricted weak type (p, p) with respect to the measure w(x) dx.