  In this paper the authors study set expansion in finite fields. Fourier
analytic proofs are given for several results recently obtained by Solymosi,
Vinh and Vu using spectral graph theory. In addition, several generalizations
of these results are given.
  In the case that $A$ is a subset of a prime field $\mathbb F_p$ of size less
than $p^{1/2}$ it is shown that $|\{a^2+b:a,b \in A\}|\geq C |A|^{147/146}$,
where $|\cdot|$ denotes the cardinality of the set and $C$ is an absolute
constant.
