At this point we have established that if $f : \{-1,1\} \to {\mathbb R}$ then for any $p \leq 2 \leq q$, \[ \|\mathrm{T}_{\sqrt{p-1}} f\|_2 \leq \|f\|_p, \qquad \|\mathrm{T}_{1/\sqrt{q-1}} f\|_q \leq \|f\|_2. \] We would like to extend these facts to the case of general $f : \{-1,1\}^n \to {\mathbb R}$; i.e., establish the $(p,2)$- [...]

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Ohad Klein: In 15c (18c in the book), I think it should be $\cap_j{V_j}$...Ohad Klein: Bracket typo: In the proof of thm 10 (12 in the book), $sgn(...Ohad Klein: Oops, my bad.Ohad Klein: I think there is a bug in ex 4 (also in the book): take for ...Ryan O'Donnell: Thanks, fixed!Ryan O'Donnell: Right!Ryan O'Donnell: Thanks! You have sharper eyes than the professional copyedi...