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

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

2010-12-14

arxiv.org/abs/1012.3146v1

Proc. Amer. Math. Soc. 140 (2012), 915-926

Mathematics

Classical Analysis and ODEs

13 pages, 2 figures

Scientific paper

10.1090/S0002-9939-2011-11078-5

Analogues of Hausdorff-Young inequalities for the Dirac scattering transform (a.k.a. SU(1,1) nonlinear Fourier transform) were first established by Christ and Kiselev [1],[2]. Later Muscalu, Tao, and Thiele [5] raised a question if 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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