Lp-estimates for Riesz transforms on forms in the Poincaré space
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 ∆...
| Autor: | |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:115172 |
| Acceso en línea: | https://ddd.uab.cat/record/115172 https://dx.doi.org/urn:doi:10.1512/iumj.2005.54.2501 |
| Access Level: | acceso abierto |
| Palabra clave: | Hodge-de Rham laplacian Sobolev spaces Riesz transforms Hyperbolic form convolution |
| Sumario: | 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. |
|---|