dc.contributor.author |
Bruna, Joaquim |
dc.date |
2005 |
dc.date.accessioned |
2021-09-09T18:36:33Z |
dc.date.available |
2021-09-09T18:36:33Z |
dc.date.issued |
2021-09-09 |
dc.identifier |
https://ddd.uab.cat/record/115172 |
dc.identifier |
10.1512/iumj.2005.54.2501 |
dc.identifier |
oai:ddd.uab.cat:115172 |
dc.identifier |
ARE-55814 |
dc.identifier |
00222518v54n1p153 |
dc.identifier |
17244365876 |
dc.identifier |
000227939500005 |
dc.identifier |
oai:egreta.uab.cat:publications/95ea348f-2d90-4b8e-bb01-b7b0dc808e28 |
dc.identifier.uri |
http://hdl.handle.net/2072/474044 |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
|
dc.relation |
Indiana University mathematics journal ; Vol. 54, No. 1 (2005), p. 153-187 |
dc.rights |
open access |
dc.rights |
Tots els drets reservats. |
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 |
dc.type |
Article |
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. |