L^p estimates for Riesz transforms on forms in the Poincare space H^n

Joaquim Bruna

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L^p estimates for Riesz transforms on forms in the Poincare space H^n

Joaquim Bruna

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Abstract

Using hyperbolic form convolution with doubly isometry-invariant kernels, the explicit expression of the inverse of the de Rham laplacian acting on m-forms in the Poincaré space is found. Also, by means of some estimates for hyperbolic singular integrals, we obtain L^p-estimates for the Riesz transforms passing from the Laplacian to other covariant derivatives, in a range of p depending on m,n. Finally, using these, it is shown that the Laplacian defines topological isomorphisms in the scale of form Sobolev spaces, for m different from n/2,(n+1)/2,(n-1)/2.

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Joaquim Bruna. 2004-11-25. L^p estimates for Riesz transforms on forms in the Poincare space H^n. https://arxiv.org/abs/math/0411569

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