Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
Riesz transforms associated to Hermite functions were introduced by S. Thangavelu, who proved that they are bounded operators on L^p(R^d ), 1 < p < ∞ . In this paper we give a different proof that allows us to show that the Lp-norms of these operators are bounded by a constant not depending on...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2004 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/101031 |
| Acceso en línea: | http://hdl.handle.net/11336/101031 |
| Access Level: | acceso abierto |
| Palabra clave: | Hermite functions https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Riesz transforms associated to Hermite functions were introduced by S. Thangavelu, who proved that they are bounded operators on L^p(R^d ), 1 < p < ∞ . In this paper we give a different proof that allows us to show that the Lp-norms of these operators are bounded by a constant not depending on the dimension d. Moreover, we define Riesz transforms of higher order and free dimensional estimates of the L^p-bounds of these operators are obtained. In order to prove the mentioned results we give an extension of the Littlewood-Paley theory that we believe of independent interest. |
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