A perturbation result for the Riesz transform

الأصل · EN

We show a perturbation result for the boundedness of the Riesz transform: if M and M₀ are complete Riemannian manifolds satisfying a Sobolev inequality of dimension n, which are isometric outside a compact set, and if the Riesz transform on M₀ is bounded on Lq, then for all n/n-2, the Riesz transform on M is bounded on Lᵖ provided that M is p-hyperbolic OR M has only one end.