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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Gautam Kamath: Is $q'$ defined here?Gautam Kamath: On this page, Hölder is displaying for me as H{ö}lder - is t...Ryan O'Donnell: Yes, you're right. This is not a well-written proof by the ...Ryan O'Donnell: Thanks, yes.Ryan O'Donnell: Yep, thanks.Ryan O'Donnell: Yep, thanks.Noam Lifshitz: I think that in exercise 23, it should be $(p,2)$ Hypercontr...