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On weighted weak type inequalities for modified Hardy operators

Author(s): F. J. Martín-Reyes; P. Ortega
Journal: Proc. Amer. Math. Soc. 126 (1998), 1739-1746.
MSC (1991): Primary 26D15
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Abstract: We characterize the pairs of weights $(w,v)$ for which the modified Hardy operator $Tf(x)=g(x)\int _{0}^{x}f$ applies $L^{p}(v)$ into weak-$L^{q}(w)$ where $g$ is a monotone function and $1\le q<p<\infty $.

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Additional Information:

F. J. Martín-Reyes
Affiliation: Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain
Email: martin@anamat.cie.uma.es

P. Ortega
Affiliation: Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain
Email: ortega@anamat.cie.uma.es

DOI: 10.1090/S0002-9939-98-04247-6
PII: S 0002-9939(98)04247-6
Keywords: Hardy operators, weights, inequalities
Received by editor(s): September 8, 1995
Received by editor(s) in revised form: December 1, 1996
Additional Notes: This research has been partially supported by D.G.I.C.Y.T. grant (PB94-1496) and Junta de Andalucía
Communicated by: J. Marshall Ash
Copyright of article: Copyright 1998, American Mathematical Society

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