  We prove an analogue of Bonami's (hypercontractive) lemma for complex-valued
functions on $\mathcal{L}(V,W)$, where $V$ and $W$ are vector spaces over a
finite field. This inequality is useful for functions on $\mathcal{L}(V,W)$
whose `generalised influences' are small, in an appropriate sense. It leads to
a significant shortening of the proof of a recent seminal result by Khot,
Minzer and Safra that pseudorandom sets in Grassmann graphs have near-perfect
expansion, which (in combination with the work of Dinur, Khot, Kindler, Minzer
and Safra) implies the 2-2 Games conjecture (the variant, that is, with
imperfect completeness).
