A sharp nonlinear Hausdorff-Young inequality for small potentials

Diogo Oliveira E Silva, Vjekoslav Kovac, Jelena Rupcic

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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 L1 norm. The proof combines perturbative techniques with the sharpened version of the linear Hausdorff-Young inequality due to Christ.
Original languageEnglish
Pages (from-to)239-253
JournalProceedings of the American Mathematical Society
Early online date3 Oct 2018
Publication statusE-pub ahead of print - 3 Oct 2018


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