A sharp nonlinear Hausdorff-Young inequality for small potentials
Classical Analysis and ODEs
2019-02-04 v2
Abstract
The nonlinear Hausdorff-Young inequality follows from the work of Christ and Kiselev. Later Muscalu, Tao, and Thiele asked if the constants can be chosen independently of the exponent. We show that the nonlinear Hausdorff-Young quotient admits an even better upper bound than the linear one, provided that the function is sufficiently small in the norm. The proof combines perturbative techniques with the sharpened version of the linear Hausdorff-Young inequality due to Christ.
Cite
@article{arxiv.1703.05557,
title = {A sharp nonlinear Hausdorff-Young inequality for small potentials},
author = {Vjekoslav Kovač and Diogo Oliveira e Silva and Jelena Rupčić},
journal= {arXiv preprint arXiv:1703.05557},
year = {2019}
}
Comments
14 pages, v2: referee's suggestions incorporated