Vector-valued extensions of operators related to the Ornstein-Uhlenbeck semigroup
We find necessary and sufficient conditions on a Banach space X in order for the vector-valued extensions of several operators associated to the Ornstein-Uhlenbeck semigroup to be of weak type (1,1) or strong type (p,p) in the range 1 < p < ∞. In this setting, we consider the Riesz transforms...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2003 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/100593 |
| Acceso en línea: | http://hdl.handle.net/11336/100593 |
| Access Level: | acceso abierto |
| Palabra clave: | Vector value operator UMD, Lusin cotype 2 and Hardy-Littlewood Orstein -Uhlenbeck https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | We find necessary and sufficient conditions on a Banach space X in order for the vector-valued extensions of several operators associated to the Ornstein-Uhlenbeck semigroup to be of weak type (1,1) or strong type (p,p) in the range 1 < p < ∞. In this setting, we consider the Riesz transforms and the Littlewood-Paley g-functions. We also deal with vector-valued extensions of some maximal operators like the maximal operators of the Ornstein-Uhlenbeck and the corresponding Poisson semigroups and the maximal function with respect to the gaussian measure. In all cases, we show that the condition on X is the same as that required for the corresponding harmonic operator: UMD, Lusin cotype 2 and Hardy-Littlewood property. In doing so, we also find some new equivalences even for the harmonic case. |
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