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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Rubio de Francia's extrapolation theorem for $ B_p$ weights


Authors: María J. Carro and María Lorente
Journal: Proc. Amer. Math. Soc. 138 (2010), 629-640
MSC (2000): Primary 26D10, 46E20
Published electronically: September 10, 2009
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Abstract: In this paper, we prove some of Rubio de Francia's extrapolation results for the class $ B_p$ of weights for which the Hardy operator is bounded on $ L^p(w)$ restricted to decreasing functions. Applications to the boundedness of operators on $ L^p_{{\rm dec}}(w)$ are given. We also present an extension to the $ B_\infty$ case and some connections with classical $ A_p$ theory.


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Additional Information

María J. Carro
Affiliation: Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08071 Barcelona, Spain
Email: carro@ub.edu

María Lorente
Affiliation: Departamento de Análisis Matemático, Universidad de Málaga, 29071 Málaga, Spain
Email: lorente@anamat.cie.uma.es

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10040-0
PII: S 0002-9939(09)10040-0
Keywords: Extrapolation, monotone functions, $B_p$ weights, Calder\'on and Riemann-Liouville operator
Received by editor(s): March 30, 2009
Received by editor(s) in revised form: May 8, 2009
Published electronically: September 10, 2009
Additional Notes: This work was supported by MTM2007-60500, by CURE 2005SGR00556 and MTM2005-08350-C03-02, and by Junta de Andalucía FQM354 and P06-FQM-01509.
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.