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A+∞ Condition

Published online by Cambridge University Press:  20 November 2018

F. J. Martín-Reyes ,
L. Pick  and
A. De La Torre
F. J. Martín-Reyes*
Affiliation:
Andlisis Matemdtico Facultad de Ciencias Universidad de Malaga 29071 Malaga Spain, e-mail: MARTIN-REYES@CCUMA UMA ES
L. Pick*
Affiliation:
Mathematical Institute of the Czechoslovak Academy of Sciencesžitna 25 115 67 Prahal, Czechoslovakia, e-mail: PICK@CSEARN.BITNET
A. De La Torre*
Affiliation:
Analisis Matemdtico Facultad de Ciencias Universidad de Malaga 29071 Malaga, Spain, e-mail:TORRE-R@CCUMA.UMA.ES
*
Current address: School of Mathematics University of Wales College of Cardiff Senghennydd Road Cardiff CF2 4AG United Kingdom, e-mail: PICKL@TAFF CARDIFF AC UK
Current address: School of Mathematics University of Wales College of Cardiff Senghennydd Road Cardiff CF2 4AG United Kingdom, e-mail: PICKL@TAFF CARDIFF AC UK
Current address: School of Mathematics University of Wales College of Cardiff Senghennydd Road Cardiff CF2 4AG United Kingdom, e-mail: PICKL@TAFF CARDIFF AC UK
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Abstract

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The good weights for the one-sided Hardy-Littlewood operators have been characterized by conditions . In this paper we introduce a new condition which is analogous to A∞. We show several characterizations of . For example, we prove that the class of weights is the union of classes. We also give a new characterization of weights. Finally, as an application of condition, we characterize the weights for one-sided fractional integrals and one-sided fractional maximal operators.

Keywords

42B25one-sided Hardy-Littlewood maximal operatorsweighted inequalitiesweightsone-sided fractional operatorsone-sided fractional maximal operatorsRiemann-Liouville fractional integral operator
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 6 , 01 December 1993 , pp. 1231 - 1244
Copyright
Copyright © Canadian Mathematical Society 1993

Footnotes

This research has been partially supported by D.G.I.C.Y.T. grant (PB88-0324) and Junta de Andalucia.

References

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