Abstract. 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 L p (w) are the Calderón weights of the class C p . We give a new characterization of the weights in C p by a single condition which allows us to see that C p 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 C p do not behave like the usual A p weights with respect to some properties and, in particular, we answer an open question on extrapolation for Muckenhoupt bases without the openness property.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.