In this section we describe a basis-free kind of “Fourier expansion” for functions on general product domains. We will refer to it as the orthogonal decomposition of $f \in L^2(\Omega^n, \pi^{\otimes n})$ though it goes by several other names in the literature: e.g., Hoeffding, Efron–Stein, or ANOVA decomposition.

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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...