Sharp bounds for fractional operator with $L^{\alpha,s}$-H\"ormander conditions
In this paper we provide the sharp bound for a fractional type operator given by a kernel satisfying the$L^{alpha,s}$-H"ormander condition and fractional size condition, $0<alpha<n$ and $1< sleq infty$. To prove this result we use a new appropriate sparse domination provided in this wo...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/196769 |
| Acceso en línea: | http://hdl.handle.net/11336/196769 |
| Access Level: | acceso abierto |
| Palabra clave: | FRACTIONAL OPERATORS FRACTIONAL $L^{S}$-HORMANDER'S CONDITION SHARP WEIGHTS INEQUALITIES SPARSE OPERATORS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | In this paper we provide the sharp bound for a fractional type operator given by a kernel satisfying the$L^{alpha,s}$-H"ormander condition and fractional size condition, $0<alpha<n$ and $1< sleq infty$. To prove this result we use a new appropriate sparse domination provided in this work. Examples of these operators include the fractional rough operators. For the case $s=infty$ we recover the sharp bound of the fractional integral, $I_{alpha}$, proved in [Lacey, M. T., Moen, K., P´erez, C., Torres, R. H. (2010). Sharp weighted bounds for fractional integral operators. Journal of Functional Analysis, 259(5), 1073-1097]. |
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