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

Abstract

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 $1\le p\le 2$. Here we give a positive answer to that question when the Euclidean real line is replaced by its Cantor group model.

13 pages, 2 figures

Cited by in corpus (2)

• A sharp nonlinear Hausdorff-Young inequality for small potentials
• Asymptotically sharp discrete nonlinear Hausdorff-Young inequalities for the SU(1,1)-valued Fourier products