Let $A \subset \mathbb{F}_q$ , a finite field with $q$ elements. We shall use Fourier analysis to see that if $\sqrt{q}<<\char93 A<<q$ , then either the sumset $A+A$ or the product set $A \cdot A$ must be much larger than $A$ . Our main tool is an incidence theorem for hyperbolas and points obtained by using classical Kloosterman sums estimates.