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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a trilinear singular integral form with determinantal kernel
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by Philip Gressman, Danqing He, Vjekoslav Kovač, Brian Street, Christoph Thiele and Po-Lam Yung PDF
Proc. Amer. Math. Soc. 144 (2016), 3465-3477 Request permission

Abstract:

We study a trilinear singular integral form acting on two- dimensional functions and possessing invariances under arbitrary matrix dilations and linear modulations. One part of the motivation for introducing it lies in its large symmetry groups acting on the Fourier side. Another part of the motivation is that this form stands between the bilinear Hilbert transforms and the first Calderón commutator, in the sense that it can be reduced to a superposition of the former, while it also successfully encodes the latter. As the main result we determine the exact range of exponents in which the $\mathrm {L}^p$ estimates hold for the considered form.
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Additional Information
  • Philip Gressman
  • Affiliation: Department of Mathematics, David Rittenhouse Lab, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104-6395
  • MR Author ID: 690453
  • Email: gressman@math.upenn.edu
  • Danqing He
  • Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
  • MR Author ID: 1059054
  • Email: dhd27@mail.missouri.edu
  • Vjekoslav Kovač
  • Affiliation: Faculty of Science, Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
  • MR Author ID: 962691
  • Email: vjekovac@math.hr
  • Brian Street
  • Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706
  • MR Author ID: 734063
  • ORCID: setImmediate$0.7188965420588604$10
  • Email: street@math.wisc.edu
  • Christoph Thiele
  • Affiliation: Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
  • Email: thiele@math.uni-bonn.de
  • Po-Lam Yung
  • Affiliation: The Chinese University of Hong Kong, Ma Liu Shui, Hong Kong
  • MR Author ID: 763642
  • ORCID: 0000-0002-0441-3625
  • Email: plyung@math.cuhk.edu.hk
  • Received by editor(s): October 5, 2015
  • Published electronically: April 13, 2016
  • Additional Notes: The first author was partially supported by the NSF grant DMS-1361697 and an Alfred P. Sloan Research Fellowship
    The second author was partially supported by the Simons Foundation Grant Number 315380
    The third author was partially supported by the Croatian Science Foundation under the project 3526
    The fourth author was partially supported by the NSF grant DMS-1401671
    The fifth author was partially supported by the Hausdorff Center for Mathematics
    The sixth author was partially supported by a direct grant for research from the Chinese University of Hong Kong (4053120)
  • Communicated by: Svitlana Mayboroda
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 3465-3477
  • MSC (2010): Primary 42B20
  • DOI: https://doi.org/10.1090/proc/13007
  • MathSciNet review: 3503714