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$ \newcommand{\R}{{\mathbb R}} $ The Hypercontractive Inequality of Bonami (1968, 1970) and Gross (1975) is equivalent to the following statement: for every $q > 2$ and every function $f : \{-1,1\}^n \to \R$ of Fourier degree at most $m$, $$ \|f \|_q \le (q-1)^{m/2} \|f\|_2. $$ The original proof of …