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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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Uniform constants in Hausdorff-Young inequalities for the Cantor group model of the scattering transform
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by Vjekoslav Kovač PDF
Proc. Amer. Math. Soc. 140 (2012), 915-926 Request permission

Abstract:

Analogues of Hausdorff-Young inequalities for the Dirac scattering transform (a.k.a. the $\mathrm {SU}(1,1)$ nonlinear Fourier transform) were first established by Christ and Kiselev. Later Muscalu, Tao, and Thiele raised a question whether the constants can be chosen uniformly in $1\leq p\leq 2$. Here we give a positive answer to that question when the Euclidean real line is replaced by its Cantor group model.
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Additional Information
  • Vjekoslav Kovač
  • Affiliation: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095-1555
  • MR Author ID: 962691
  • Email: vjekovac@math.ucla.edu
  • Received by editor(s): December 14, 2010
  • Published electronically: July 13, 2011
  • Communicated by: Michael T. Lacey
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 915-926
  • MSC (2010): Primary 34L25; Secondary 42A38
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11078-5
  • MathSciNet review: 2869075