arXiv subjects

Jelena Rupčić

Publications and source records attributed to Jelena Rupčić.

4 recordsLinked to original sources

arXiv2026

Hausdorff-Young inequalities for $\mathrm{SU}(1,1)$ Fourier products indexed by binary cubes

We study nonlinear logarithmic Hausdorff-Young inequalities with constant $1$ for $\mathrm{SU}(1,1)$-valued Fourier products indexed by binary cubes. The inequalities are proved for the optimal range of exponents, extending into the region $1/p + 1/q < 1$. The proof combines majorization, a known sharp two-point inequality, and tree iteration. We also obtain the corresponding chain inequality and nonlinear bounds for generating functions of alternating chains, recovering the known sharp bounds for additive energies on the binary cube as the amplitudes vanish.

math.CA↗

arXiv2022

Asymptotically sharp discrete nonlinear Hausdorff-Young inequalities for the SU(1,1)-valued Fourier products

We work in a discrete model of the nonlinear Fourier transform (following the terminology of Tao and Thiele), which appears in the study of orthogonal polynomials on the unit circle. The corresponding nonlinear variant of the Hausdorff-Young inequality can be deduced by adapting the ideas of Christ and Kiselev to the present discrete setting. However, the behavior of sharp constants remains largely unresolved. In this short note we give two results on these constants, after restricting our attention to either sufficiently small sequences or to sequences that are far from being the extremizers of the linear Hausdorff-Young inequality.

math.CA↗

arXiv2019

Convergence of lacunary SU(1,1)-valued trigonometric products

This note attempts to study lacunary trigonometric products with values in the matrix group SU(1,1) in analogy with lacunary trigonometric series. The central questions are the characterization of their convergence in an appropriately define $L^p$-metric and the characterization of their convergence almost everywhere. These can be interpreted as nonlinear analogues of the classical results by Zygmund and Kolmogorov.

math.CA↗

arXiv2018

A sharp nonlinear Hausdorff-Young inequality for small potentials

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 $L^1$ norm. The proof combines perturbative techniques with the sharpened version of the linear Hausdorff-Young inequality due to Christ.

math.CA↗