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

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dc.creatorBruna, Joaquim
dc.date2004-11-25
dc.date.accessioned2026-07-07T05:14:42Z
dc.date.available2026-07-07T05:14:42Z
dc.descriptionUsing 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.
dc.descriptionTo appear in Indiana Univ. Math. J
dc.identifierhttps://arxiv.org/abs/math/0411569
dc.identifierhttp://arxiv.org/abs/math/0411569
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73374
dc.subjectAnalysis of PDEs
dc.subjectDifferential Geometry
dc.subject53C21, 58J05, 58J50, 58J70
dc.titleL^p estimates for Riesz transforms on forms in the Poincare space H^n
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