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Weighted $ L^2$ inequalities for square functions


Authors: Rodrigo Bañuelos and Adam Osȩkowski
Journal: Trans. Amer. Math. Soc. 370 (2018), 2391-2422
MSC (2010): Primary 42B20; Secondary 46E30
DOI: https://doi.org/10.1090/tran/7056
Published electronically: November 7, 2017
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Abstract | References | Similar Articles | Additional Information

Abstract: Using the Bellman function approach, we present new proofs of
weighted $ L^2$ inequalities for square functions, with the optimal dependence on the $ A_2$ characteristics of the weight and further explicit constants. We study the estimates both in the analytic and probabilistic context, and, as an application, obtain related estimates for the classical Lusin and Littlewood-Paley square functions.


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Additional Information

Rodrigo Bañuelos
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: banuelos@math.purdue.edu

Adam Osȩkowski
Affiliation: Department of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
Email: ados@mimuw.edu.pl

DOI: https://doi.org/10.1090/tran/7056
Keywords: Square function, dyadic, Bellman function, best constants
Received by editor(s): March 14, 2016
Received by editor(s) in revised form: July 13, 2016
Published electronically: November 7, 2017
Additional Notes: The first author was supported in part by NSF grant #0603701-DMS
The second author was supported in part by National Science Center Poland (Narodowe Center Nauki) grant DEC-2014/14/E/ST1/00532.
Article copyright: © Copyright 2017 American Mathematical Society

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