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ISSN 1088-6826(e) ISSN 0002-9939(p)

Rubio de Francia's extrapolation theorem for weights

Author(s): María J. Carro; María Lorente
Journal: Proc. Amer. Math. Soc. 138 (2010), 629-640.
MSC (2000): Primary 26D10, 46E20
Posted: September 10, 2009
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Abstract: In this paper, we prove some of Rubio de Francia's extrapolation results for the class of weights for which the Hardy operator is bounded on 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 theory.

References:

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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: 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
Posted: 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
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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