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arXiv · 0907.0856

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

Pengtao Li·Zhichun Zhai
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Abstract

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

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Pengtao Li, Zhichun Zhai. 2009-07-05. Riesz transforms on Q-type spaces with application to quasi-geostrophic equation. https://arxiv.org/abs/0907.0856

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