Riesz Transforms on Compact Riemannian Symmetric Spaces of Rank One
In this paper we prove mixed norm estimates for Riesz transforms related to Laplace–Beltrami operators on compact Riemannian symmetric spaces of rank one. These operators are closely related to the Riesz transforms for Jacobi polynomials expansions. The key point is to obtain sharp estimates for the...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universidad de La Rioja (UR) |
| Repositorio: | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| OAI Identifier: | oai:portal.dialnet.es:doc/5bbc6817b750603269e80263 |
| Acceso en línea: | https://investigacion.unirioja.es/documentos/5bbc6817b750603269e80263 |
| Access Level: | acceso abierto |
| Palabra clave: | Analysis on compact Riemannian symmetric spaces of rank 1 Jacobi expansions Laplace–Beltrami operator mixed norm spaces Riesz transform Rubio de Francia extrapolation theorem |
| Sumario: | In this paper we prove mixed norm estimates for Riesz transforms related to Laplace–Beltrami operators on compact Riemannian symmetric spaces of rank one. These operators are closely related to the Riesz transforms for Jacobi polynomials expansions. The key point is to obtain sharp estimates for the kernel of the Jacobi–Riesz transforms with uniform control on the parameters, together with an adaptation of Rubio de Francia’s extrapolation theorem. The latter results are of independent interest. © 2015, Springer Basel. |
|---|