Singular measures and convolution operators

We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type (1, 1) inequalities. As an application, we prove that the best constants for the centered Hardy-Littlewood maximal operator associated w...

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Detalles Bibliográficos
Autores: Aldaz, J.M. [0000-0001-8472-2606], Varona, J.L. [0000-0002-2023-9946]
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2007
País:España
Institución:Universidad de La Rioja (UR)
Repositorio:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc6a1fb750603269e82769
Acceso en línea:https://investigacion.unirioja.es/documentos/5bbc6a1fb750603269e82769
Access Level:acceso abierto
Palabra clave:Convolution operators
Hardy-Littlewood maximal function
Singular measures
Weak type inequalities
Descripción
Sumario:We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type (1, 1) inequalities. As an application, we prove that the best constants for the centered Hardy-Littlewood maximal operator associated with parallelotopes do not decrease with the dimension. © Springer-Verlag Berlin Heidelberg 2007.