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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Weighted inequalities for some one-sided operators


Authors: M. Lorente and A. de la Torre
Journal: Proc. Amer. Math. Soc. 124 (1996), 839-848
MSC (1991): Primary 26A33
DOI: https://doi.org/10.1090/S0002-9939-96-03089-4
MathSciNet review: 1317510
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Abstract: We give a characterization of the pairs of weights $(u,v)$ such that the Weyl fractional integral operator maps $L^p(vdx)$ into weak $L^q(udx)$, $1<p\leq q<\infty $ or $p=1<q<\infty $. For the case $p<q$ we give necessary and sufficient conditions for the weak type of a maximal operator that includes as particular cases the Weyl fractional integral, the dual of the Hardy operator and the fractional one-sided maximal operator. As a consequence we give a new characterization of the pairs of weights for which the fractional one-sided maximal operator is bounded.


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Additional Information

M. Lorente
Affiliation: Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain
Email: m_lorente@ccuma.sci.uma.es

A. de la Torre
Affiliation: Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain
Email: torre_r@ccuma.sci.uma.es

DOI: https://doi.org/10.1090/S0002-9939-96-03089-4
Keywords: Weyl fractional integral, weights
Received by editor(s): March 15, 1994
Received by editor(s) in revised form: September 14, 1994
Additional Notes: This research has been supported by D.G.I.C.Y.T. grant (PB91-0413) and Junta de Andalucía.
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society