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arXiv · 1704.00688

A variational nonlinear Hausdorff-Young inequality in the discrete setting

Diogo Oliveira e Silva
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Abstract

Following the works of Lyons and Oberlin, Seeger, Tao, Thiele and Wright, we relate the variation of certain discrete curves on the Lie group $\text{SU}(1,1)$ 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 $\text{SU}(1,1)$.

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Diogo Oliveira e Silva. 2017-04-03. A variational nonlinear Hausdorff-Young inequality in the discrete setting. https://arxiv.org/abs/1704.00688

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