Finite reflection groups and graph norms

Given a graph H on vertex set {1,2,⋯,n} and a function f:[0,1]2→R, define ∥f∥H:=∣∣∣∣∫∏ij∈E(H)f(xi,xj)dμ|V(H)|∣∣∣∣1/|E(H)|, where μ is the Lebesgue measure on [0,1]. We say that H is norming if ∥⋅∥H is a semi-norm. A similar notion ∥⋅∥r(H) is defined by ∥f∥r(H):=∥|f|∥H and H is said to be we...