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Transactions of the American Mathematical Society

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Endpoint estimates for Rubio de Francia operators


Authors: María J. Carro and Carlos Domingo-Salazar
Journal: Trans. Amer. Math. Soc. 371 (2019), 1621-1648
MSC (2010): Primary 42B99, 46E30
DOI: https://doi.org/10.1090/tran/7328
Published electronically: September 20, 2018
MathSciNet review: 3894029
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Abstract: The extrapolation theory of Rubio de Francia provides a tool to obtain $ A_p$ weighted estimates on $ L^p$ spaces for every $ 1<p<\infty $, starting from information at a single $ 1<p_0<\infty $. However, the endpoint case $ p=1$ cannot be reached in general. Classical extrapolation arguments in the sense of Yano can be added to this setting to deduce results close to $ L^1$ without weights. In this paper, we present different approaches that produce endpoint estimates with respect to the whole $ A_1$ class. We give applications to the Carleson operator and maximally modulated singular integrals among others.


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Additional Information

María J. Carro
Affiliation: Departament de Matemàtiques i Informàtica, Universitat de Barcelona, 08007 Barcelona, Spain
Email: carro@ub.edu

Carlos Domingo-Salazar
Affiliation: Departament de Matemàtiques i Informàtica, Universitat de Barcelona, 08007 Barcelona, Spain
Email: domingo@ub.edu

DOI: https://doi.org/10.1090/tran/7328
Keywords: Rubio de Francia operators, weighted estimates, $A_p$ weights, Yano's extrapolation
Received by editor(s): July 13, 2016
Received by editor(s) in revised form: May 27, 2017, and June 20, 2017
Published electronically: September 20, 2018
Additional Notes: The authors were supported by Spanish Government grants MTM2016-75196-P and R&D (MDM-2014-0445), and by the Catalan Autonomous Government grant 2014SGR289
Article copyright: © Copyright 2018 American Mathematical Society