Sharp Hypercontractivity for Global Functions

Nathan Keller, Noam Lifshitz, Omri Marcus

For a function $f$ on the hypercube $\{0,1{\}}^n$ with Fourier expansion $f={\sum }_{S\subseteq [n]}\hat{f}(S){\chi }_S$, the hypercontractive inequality allows bounding norms of $T_ρf=\sum_Sρ^…