Extrapolation for classes of weights related to a family of operators

BONGIOANNI, BRUNO; CABRAL, ENRIQUE ADRIÁN; HARBOURE, ELEONOR

El Escorial - Madrid

Conferencia; 9th International Conference on Harmonic Analysis and Partial Differential Equations; 2012

Universidad Autonoma de Madrid - CSIC

In this work we deal with the extrapolation property for classes of weights that arise from the L^p boundedness of a one-parameter family of maximal operators, rather than a single operator like in the case of  Muckenhoupt classes A_p. The starting point for the extrapolation can be the knowledge of boundedness on a particular Lebesgue space as well as the boundedness on the extremal case L^infty with some BMO type inequalities. Our approach models the situation of weights appearing in the context of the analysis related to the Schrödinger operator  - Laplaciano + V. We apply the extrapolation results to obtain weighted scalar and vector valued inequalities for some operators associated to - Laplaciano + V.