Lemma 4.10 (Gowers–Cauchy–Schwarz Inequality). Assuming that:

  • fπœ€:Gβ†’β„‚, πœ€βˆˆ{0,1}3

Then
|⟨(fπœ€)πœ€βˆˆ{0,1}3⟩U3(G)β‰€βˆπœ€βˆˆ{0,1}3βˆ₯fπœ€βˆ₯U3(G).