Riesz transforms on Q-type spaces with application to quasi-geostrophic equation

Abstract

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 $Q_{\alpha }^{\beta ,-1}({\mathbb{R}}^2).$

18 pages, submitted