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:2-4-hypercon-k} \|\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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Ryan O'Donnell: Yes, thanks! Sorry for the delay in replying.Ryan O'Donnell: No, it's definitely messed up. Will fix!Ryan O'Donnell: Thanks!Ryan O'Donnell: Hi Amir. It's just a 'dummy variable'; in some sense an X's...Ryan O'Donnell: Right, or I guess I can just switch 'codimension' to 'dimens...Ryan O'Donnell: Yep, thanks!Ryan O'Donnell: Thanks, seems like I spotted this one myself too. (Not corr...