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Norm estimates for the Hardy operator in terms of $ B_p$ weights


Authors: Santiago Boza and Javier Soria
Journal: Proc. Amer. Math. Soc. 145 (2017), 2455-2465
MSC (2010): Primary 26D15, 42B25, 46E30
DOI: https://doi.org/10.1090/proc/13604
Published electronically: February 20, 2017
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Abstract: We study the explicit dependence of the Hardy operator norm, acting on non-increasing functions in $ L^p(w)$ or $ L^{p,\infty }(w)$, in terms of the $ B_p$-constant of the weight $ w$.


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Additional Information

Santiago Boza
Affiliation: Department of Applied Mathematics IV, EETAC, Polytechnical University of Catalonia, E-08860 Castelldefels, Spain
Email: santiago.boza@upc.edu

Javier Soria
Affiliation: Department of Mathematics and Informatics, University of Barcelona, Gran Via 585, E-08007 Barcelona, Spain
Email: soria@ub.edu

DOI: https://doi.org/10.1090/proc/13604
Keywords: Hardy operator, $B_p$-weights.
Received by editor(s): May 26, 2016
Published electronically: February 20, 2017
Additional Notes: Both authors have been partially supported by the Spanish Government grants MTM2013-40985-P and MTM2016-75196-P and the Catalan autonomous government grant 2014SGR289.
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2017 American Mathematical Society