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[...] With the $(2,q)$ and $(p,2)$Hypercontractivity Theorems in hand, let’s revisit some applications we saw in Sections 1 and 2. [...] In this section we prove two theorems about the degree$1$ Fourier weight of boolean functions: \[ \mathbf{W}^{1}[f] = \sum_{i=1}^n \widehat{f}(i)^2. \] [...] 

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