Convolution of discrete measures on linear groups

Let p, q ∈ R such that 1 0 such that for f ∈ p(G) f ∗ f 1/2 q C f 1−τ p f p τ , where the maximum in (∗) is taken over all abelian subgroups G1 0 and 1 > τ = τp > 0 such that if f ∈ p(SL3(Z)), then f ∗ f 1/2 q C f 1−τ p f p τ , where the maximum in (∗) is taken over all nilpotent subgroups G1 of SL3(Z) and x ∈ SL3(Z).