On fractional operators with more than one singularity

Let 0 ≤ α < n, m ∈ N and let Tα,m be an integral operator given by a kernel of the form K(x, y) = k1(x − A1y)k2(x − A2y) . . . km(x − Amy), where Ai are invertible matrices and each ki satisfies a fractional size and a generalized fractional H¨ormander condition that depends on α. In this survey,...

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Detalles Bibliográficos
Autores: Riveros, Maria Silvina, Vidal, Raúl Emilio
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/231972
Acceso en línea:http://hdl.handle.net/11336/231972
Access Level:acceso abierto
Palabra clave:Maximal operators
Calderón-Zygmund Operators
Fractional Operators
Generalized Hörmander's condition
Weighted innequalities
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:Let 0 ≤ α < n, m ∈ N and let Tα,m be an integral operator given by a kernel of the form K(x, y) = k1(x − A1y)k2(x − A2y) . . . km(x − Amy), where Ai are invertible matrices and each ki satisfies a fractional size and a generalized fractional H¨ormander condition that depends on α. In this survey, written in honour to Eleonor Harboure, we collect several results about boundedness in different spaces of the operator Tα,m, obtained along the last 35 years by several members of the Analysis Group of FAMAF, UNC.