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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniform constants in Hausdorff-Young inequalities for the Cantor group model of the scattering transform


Author: Vjekoslav Kovač
Journal: Proc. Amer. Math. Soc. 140 (2012), 915-926
MSC (2010): Primary 34L25; Secondary 42A38
Published electronically: July 13, 2011
MathSciNet review: 2869075
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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
Email: vjekovac@math.ucla.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11078-5
PII: S 0002-9939(2011)11078-5
Received by editor(s): December 14, 2010
Published electronically: July 13, 2011
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.