Extrapolation for classes of weights related to a family of operators

B. BONGIOANNI, A. CABRAL AND E. HARBOURE

El Escorial, Madrid

Congreso; 9th International Conference on Harmonic Analysis and Partial Differential Equations El Escorial; 2012

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 Schr\"odinger operator $-\Delta+V$ (see \cite{BHS}). We apply the extrapolation results to obtain weighted scalar and vector valued inequalities for some operators associated to $-\Delta+V$