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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Bilinear representation theorem
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by Kangwei Li, Henri Martikainen, Yumeng Ou and Emil Vuorinen PDF
Trans. Amer. Math. Soc. 371 (2019), 4193-4214 Request permission

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
  • MR Author ID: 977289
  • 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
  • MR Author ID: 963282
  • Email: henri.martikainen@helsinki.fi
  • Yumeng Ou
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
  • MR Author ID: 1112799
  • 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
  • MR Author ID: 1178205
  • ORCID: 0000-0001-8986-0725
  • Email: emil.vuorinen@helsinki.fi
  • 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.
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 4193-4214
  • MSC (2010): Primary 42B20
  • DOI: https://doi.org/10.1090/tran/7505
  • MathSciNet review: 3917220