Lp-estimates for Riesz transforms on forms in the Poincare space

Using hyperbolic form convolution with doubly isometry-invariant kernels, the explicit expression of the inverse of the de Rham laplacian Delta acting on m-forms in the Poincare space H-n is found. Also, by means of some estimates for hyperbolic singular integrals, LP-estimates for the Riesz transforms del(i)Delta(-1), i <= 2, in a range of p depending on m,n are obtained. Finally, using these, it is shown that A defines topological isomorphisms in a scale of Sobolev spaces H-m,p(s) (H-n) in case m not equal (n +/- 1)/2, n/2.