A variational nonlinear Hausdorff–Young inequality in the discrete setting

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 $\mathrm{SU}(1,1)$.

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Received 28 August 2017

Accepted 16 November 2017

Published 25 March 2019