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...

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Detalles Bibliográficos
Autores: Ibañez Firnkorn, Gonzalo Hugo, Riveros, María Silvina, Vidal, Raúl Emilio
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
Descripción
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].