  We study correlation bounds under pairwise independent distributions for
functions with no large Fourier coefficients. Functions in which all Fourier
coefficients are bounded by $\delta$ are called $\delta$-{\em uniform}. The
search for such bounds is motivated by their potential applicability to
hardness of approximation, derandomization, and additive combinatorics.
  In our main result we show that $\E[f_1(X_1^1,...,X_1^n) ...
f_k(X_k^1,...,X_k^n)]$ is close to 0 under the following assumptions:
  1. The vectors $\{(X_1^j,...,X_k^j) : 1 \leq j \leq n\}$ are i.i.d, and for
each $j$ the vector $(X_1^j,...,X_k^j)$ has a pairwise independent
distribution.
  2. The functions $f_i$ are uniform.
  3. The functions $f_i$ are of low degree.
  We compare our result with recent results by the second author for low
influence functions and to recent results in additive combinatorics using the
Gowers norm. Our proofs extend some techniques from the theory of
hypercontractivity to a multilinear setup.
