A sharp nonlinear Hausdorff–Young inequality for small potentials

Kovač, Vjekoslav; Oliveira e Silva, Diogo; Rupčić, Jelena

doi:10.1090/proc/14268

A sharp nonlinear Hausdorff–Young inequality for small potentials
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by Vjekoslav Kovač, Diogo Oliveira e Silva and Jelena Rupčić

Proc. Amer. Math. Soc. 147 (2019), 239-253

DOI: https://doi.org/10.1090/proc/14268

Published electronically: October 3, 2018

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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 $\operatorname {L}^1$-norm. The proof combines perturbative techniques with the sharpened version of the linear Hausdorff–Young inequality due to Christ.

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