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

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

2009-07-05

arxiv.org/abs/0907.0856v1

Mathematics

Analysis of PDEs

18 pages, submitted

Scientific paper

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

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