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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Noam Lifshitz: In corollary 17, should it be $\widehat{\mathrm{Maj}_n}(S) =...Ohad Klein: In 49 (56 in the book), it looks like a typo: $E[f_i(y^(j))]...Ryan O'Donnell: Hope so; I'm quite happy with it so far. (Thanks to all who...Yi Zhang: I got it now!!Yi Zhang: I wonder what happens with cross derivatives, for example ho...David Williamson: I wished we had done this request for names/emails when we m...Ryan O'Donnell: Thanks! It's corrected in the book.