Mathematical Research Letters

Volume 25 (2018)

Number 6

A variational nonlinear Hausdorff–Young inequality in the discrete setting

Pages: 1993 – 2015

DOI: https://dx.doi.org/10.4310/MRL.2018.v25.n6.a15

Author

Diogo Oliveira e Silva (Hausdorff Center for Mathematics, University of Bonn, Germany)

Abstract

Following the works of Lyons [9, 10] and Oberlin, Seeger, Tao, Thiele and Wright [14], we relate the variation of certain discrete curves on the Lie group $\mathrm{SU}(1,1)$ to the corresponding variation of their linearized versions on the Lie algebra. Combining this with a discrete variational Menshov–Paley–Zygmund theorem, we establish a variational Hausdorff–Young inequality for a discrete version of the nonlinear Fourier transform on $\mathrm{SU}(1,1)$.

Received 28 August 2017

Published 25 March 2019