Publication Date: 2012.
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.
Author affiliation: Duoandikoetxea, Javier. Universidad del País Vasco; España
Author affiliation: Martín Reyes, Francisco J.. Universidad de Málaga; España
Author affiliation: 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
Repository: CONICET Digital (CONICET). Consejo Nacional de Investigaciones Científicas y Técnicas