Hausdorff-Young inequalities for SU(1,1) Fourier products indexed by binary cubes

@misc{crmaric2026hausdorffyoung,
  title = {{Hausdorff-Young inequalities for $\mathrmSU(1,1)$ Fourier products indexed by binary cubes}},
  author = {Tonći Crmarić and Jelena Rupčić},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29953},
  eprint = {2609.29953},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29953},
}

TY  - UNPB
TI  - Hausdorff-Young inequalities for SU(1,1) Fourier products indexed by binary cubes
AU  - Tonći Crmarić
AU  - Jelena Rupčić
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.29953
UR  - https://arxiv.org/abs/2609.29953
AB  - We study nonlinear logarithmic Hausdorff-Young inequalities with constant $1$ for 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.
ER  -