科研之友
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摘要
Let M be a smooth connected noncompact manifold endowed with a smooth measure mu and a smooth locally subelliptic diffusion operator L satisfying L1=0, and that is symmetric with respect to mu. We show that if L satisfies, with a nonnegative curvature parameter (1), the generalized curvature inequality in (2.9), then the Riesz transform is bounded in L-p(M) for every p > 1, that is
parallel to root Gamma((-L)(-1/2)f)parallel to(p) <= C-p parallel to f parallel to(p,) f is an element of c(0)(infinity)(M)
where Gamma is the carre du champ associated to L. Our results apply in particular to all Sasakian manifolds whose horizontal Tanaka-Webster Ricci curvature is nonnegative, all Carnot groups with step two, and wide subclasses of principal bundles over Riemannian manifolds whose Ricci curvature is nonnegative.
- 出版日期2013
