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Transactions of the American Mathematical Society

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Bilinear representation theorem


Authors: Kangwei Li, Henri Martikainen, Yumeng Ou and Emil Vuorinen
Journal: Trans. Amer. Math. Soc. 371 (2019), 4193-4214
MSC (2010): Primary 42B20
DOI: https://doi.org/10.1090/tran/7505
Published electronically: September 7, 2018
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Abstract: We represent a general bilinear Calderón-Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so-called sparse $ T1$ theorem for bilinear singular integrals.


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Additional Information

Kangwei Li
Affiliation: BCAM (Basque Center for Applied Mathematics), Alameda de Mazarredo 14, 48009 Bilbao, Spain
Email: kli@bcamath.org

Henri Martikainen
Affiliation: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 University of Helsinki, Finland
Email: henri.martikainen@helsinki.fi

Yumeng Ou
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
Email: yumengou@mit.edu

Emil Vuorinen
Affiliation: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 University of Helsinki, Finland
Email: emil.vuorinen@helsinki.fi

DOI: https://doi.org/10.1090/tran/7505
Keywords: Dyadic analysis, Calder\'on--Zygmund operators, model operators, dyadic shifts, bilinear analysis, representation theorems, $T1$ theorems, weighted theory
Received by editor(s): June 19, 2017
Received by editor(s) in revised form: December 3, 2017
Published electronically: September 7, 2018
Additional Notes: The first author was supported by Juan de la Cierva—Formación 2015 FJCI-2015-24547, by the Basque Government through the BERC 2014-2017 program, and by Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323. The second author was supported by the Academy of Finland through Grants No. 294840 and No. 306901. The third author was supported by the National Science Foundation under Grant No. DMS-1440140.
Article copyright: © Copyright 2018 American Mathematical Society