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...

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Detalles Bibliográficos
Autores: Harboure, Eleonor Ofelia, Rosa, L. de, Segovia Fernandez, Carlos, Torrea Hernández, José Luis
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
Descripción
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.