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A new proof of the characterization of the weighted Hardy inequality

Published online by Cambridge University Press:  12 July 2007

A. L. Bernardis ,
F. J. Martí;n-Reyes  and
P. Ortega Salvador
A. L. Bernardis
Affiliation:
IMAL-CONICET, Güemes 3450, (3000) Santa Fe, Argentina (bernard@ceride.gov.ar)
F. J. Martí;n-Reyes
Affiliation:
Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain (martin_reyes@uma.es)
P. Ortega Salvador
Affiliation:
Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain (ortega@anamat.cie.uma.es)
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Abstract

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Maz'ja and Sinnamon proved a characterization of the boundedness of the Hardy operator from Lp(v) into Lq(w) in the case 0 < q < p, 1 < p < ∞. We present here a new simple proof of the sufficiency part of that result.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 5 , October 2005 , pp. 941 - 945
Copyright
Copyright © Royal Society of Edinburgh 2005