Weak and strong $A_p$-$A_\infty$ estimates for square functions and related operators
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- by Tuomas P. Hytönen and Kangwei Li PDF
- Proc. Amer. Math. Soc. 146 (2018), 2497-2507 Request permission
Abstract:
We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound $[w]_{A_p}^{1/p}[w]_{A_\infty }^{1/2-1/p}\lesssim [w]_{A_p}^{1/2}$ for the weak type norm of square functions on $L^p(w)$ for $p>2$; previously, such a bound was only known with a logarithmic correction. By the same approach, we also recover several related results in a streamlined manner.References
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Additional Information
- Tuomas P. Hytönen
- Affiliation: Department of Mathematics and Statistics, P.O.B. 68 (Gustaf Hällströmin katu 2b), FI-00014 University of Helsinki, Finland
- Email: tuomas.hytonen@helsinki.fi
- Kangwei Li
- Affiliation: Department of Mathematics and Statistics, P.O.B. 68 (Gustaf Hällströmin katu 2b), FI-00014 University of Helsinki, Finland
- Address at time of publication: BCAM–Basque Center for Applied Mathematics, Mazarredo, 14. 48009 Bilbao, Basque Country, Spain
- MR Author ID: 977289
- Email: kangwei.nku@gmail.com, kli@bcamath.org
- Received by editor(s): September 22, 2015
- Received by editor(s) in revised form: July 26, 2017
- Published electronically: February 28, 2018
- Additional Notes: The authors were supported by the European Union through the ERC Starting Grant “Analytic-probabilistic methods for borderline singular integrals”. They are members of the Finnish Centre of Excellence in Analysis and Dynamics Research.
- Communicated by: Ken Ono
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2497-2507
- MSC (2010): Primary 42B25
- DOI: https://doi.org/10.1090/proc/13908
- MathSciNet review: 3778152