Contents Online
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
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
Accepted 16 November 2017
Published 25 March 2019