Calderón weights as Muckenhoupt weights

Authors
Duoandikoetxea, Javier; Martín Reyes, Francisco J.; Ombrosi, Sheldy Javier
Publication Year
2012
Language
English
Format
article
Status
Published version
Description
The Calderón operator S is the sum of the the Hardy averaging operator and its adjoint. The weights w for which S is bounded on Lp (w) are the Calderón weights of the class Cp. We give a new characterization of the weights in Cp by a single condition which allows us to see that Cp is the class of Muckenhoupt weights associated to a maximal operator defined through a basis in (0, ∞). The same condition characterizes the weighted weaktype inequalities for 1 < p < ∞, but that the weights for the strong type and the weak type differ for p = 1. We also prove that the weights in Cp do not behave like the usual Ap weights with respect to some properties and, in particular, we answer an open question on extrapolation for Muckenhoupt bases without the openness property.
Fil: Duoandikoetxea, Javier. Universidad del País Vasco; España
Fil: Martín Reyes, Francisco J.. Universidad de Málaga; España
Fil: Ombrosi, Sheldy Javier. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina
Subject
CALDERÓN OPERATOR
WEIGHTED INEQUALITIES
MAXIMAL OPERATOR
MUCKENHOUPT BASES
Matemática Pura
Matemáticas
CIENCIAS NATURALES Y EXACTAS
Access level
Open access
License
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repository
CONICET Digital (CONICET)
Institution
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identifier
oai:ri.conicet.gov.ar:11336/15499