## Bounds of Riesz transforms on L p spaces for second order elliptic operators

Venue: | Ann. Inst. Fourier |

Citations: | 10 - 1 self |

### BibTeX

@ARTICLE{Shen_boundsof,

author = {Zhongwei Shen},

title = {Bounds of Riesz transforms on L p spaces for second order elliptic operators},

journal = {Ann. Inst. Fourier},

year = {},

pages = {173--197}

}

### OpenURL

### Abstract

Abstract. Let L = −div(A(x)∇) be a second order elliptic operator with real, symmetric, bounded measurable coefficients on R 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 ∇(L) −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 MO coefficients. The range of p is sharp. The closely related boundedness of ∇(L) −1/2 on weighted L 2 spaces is also studied. 1.