p-Regularity and Weights for Operators Between L-p-Spaces

Abstract

[EN] We explore the connection between p-regular operators on Banach function spaces and weighted p-estimates. In particular, our results focus on the following problem. Given finite measure spaces mu and nu, let T be an operator defined from a Banach function space X(nu) and taking values on L-p(vd mu) for v in certain family of weights V subset of L-1(mu)+ we analyze the existence of a bounded family of weights W subset of L-1(nu)+ such that for every v is an element of V there is w is an element of W in such a way that T : L-p(wd nu) -> L-p (vd mu) is continuous uniformly on V. A condition for the existence of such a family is given in terms of p-regularity of the integration map associated to a certain vector measure induced by the operator T.