With the $(2,q)$ and $(p,2)$Hypercontractivity Theorems in hand, let’s revisit some applications we saw in Sections 1 and 2.
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With the $(2,q)$ and $(p,2)$Hypercontractivity Theorems in hand, let’s revisit some applications we saw in Sections 1 and 2. [...] An immediate consequence of the Bonami Lemma is that for any $f : \{1,1\}^n \to {\mathbb R}$ and $k \in {\mathbb N}$, \begin{equation} \label{eqn:24hyperconk} \\mathrm{T}_{1/\sqrt{3}} f^{=k}\_4 = \tfrac{1}{\sqrt{3}^k} \f^{=k}\_4 \leq \f^{=k}\_2. \end{equation} [...] 

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