  In this paper, we prove the boundedness of Riesz transforms
$\partial_{j}(-\Delta)^{-1/2}$ ($j=1,2,...,n$) on the Q-type spaces
$Q_{\alpha}^{\beta}(\mathbb{R}^{n})$. As an application, we get the
well-posedness and regularity of the quasi-geostrophic equation with initial
data in $Q_{\alpha}^{\beta,-1}(\mathbb{R}^{2}).$
