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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 inequali...