A sharp nonlinear Hausdorff-Young inequality for small potentials
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Colleges, School and Institutes
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.
|Journal||Proceedings of the American Mathematical Society|
|Early online date||3 Oct 2018|
|Publication status||E-pub ahead of print - 3 Oct 2018|