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Bounds of Riesz Transforms on L p Spaces for Second Order Elliptic Operators

Zhongwei Shen (2005)

Annales de l’institut Fourier

Let = -div ( A ( x ) ) be a second order elliptic operator with real, symmetric, bounded measurable coefficients on n or on a bounded Lipschitz domain subject to Dirichlet boundary condition. For any fixed p > 2 , a necessary and sufficient condition is obtained for the boundedness of the Riesz transform ( ) - 1 / 2 on the L p space. As an application, for 1 < p < 3 + ϵ , we establish the L p boundedness of Riesz transforms on Lipschitz domains for operators with V M O coefficients. The range of p is sharp. The closely related boundedness of ...

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