dc.contributor.author
Bruna, Joaquim
dc.identifier
https://ddd.uab.cat/record/115172
dc.identifier
urn:10.1512/iumj.2005.54.2501
dc.identifier
urn:oai:ddd.uab.cat:115172
dc.identifier
urn:recercauab:ARE-55814
dc.identifier
urn:articleid:00222518v54n1p153
dc.identifier
urn:scopus_id:17244365876
dc.identifier
urn:wos_id:000227939500005
dc.identifier
urn:oai:egreta.uab.cat:publications/95ea348f-2d90-4b8e-bb01-b7b0dc808e28
dc.description.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 Hn is found. Also, by means of some estimates for hyperbolic singular integrals, Lp-estimates for the Riesz transforms ∆i∆Ñ-1, i ≤ 2, in a range of p depending on m, n are obtained. Finally, using these, it is shown that ∆ defines topological isomorphisms in a scale of Sobolev spaces Hs mp ( Hn) in case m≠ ( n ± 1) /2, n/2.
dc.format
application/pdf
dc.relation
Indiana University mathematics journal ; Vol. 54, No. 1 (2005), p. 153-187
dc.rights
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dc.rights
https://rightsstatements.org/vocab/InC/1.0/
dc.subject
Hodge-de Rham laplacian
dc.subject
Sobolev spaces
dc.subject
Riesz transforms
dc.subject
Hyperbolic form convolution
dc.title
Lp-estimates for Riesz transforms on forms in the Poincaré space
