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

2009/07/05 by Pengtao Li, Li, Pengtao, Zhichun Zhai +1 · 1 citation
Mathematics · #35Q30 #42B35 #46E30 #76D03 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0907.0856

openalex publication_date 2009/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the boundedness of Riesz transforms ∂_j(-Δ)^-1/2 (j=1,2,...,n) on the Q-type spaces Q_α^β(ℝⁿ). As an application, we get the well-posedness and regularity of the quasi-geostrophic equation with initial data in Q_α^β,-1(ℝ²).

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• Fractional Heat Semigroup Characterization of Distances from Functions in Lipschitz Spaces to Their Subspaces

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