Extrapolation for Classes of Weights Related to a Family of Operators and Applications

BONGIOANNI, B. ; CABRAL, A. ; HARBOURE, E

POTENTIAL ANALYSIS

SPRINGER

Lugar: Berlin; Año: 2012 vol. 38 p. 1207 - 1232

0926-2601

In this work we give extrapolation results on weighted Lebesgue spaces for weights associated to a family of operators. 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 $L^infty$. This analysis can be applied to a variety of operators appearing in the context of a Schr"odinger operator $(-Delta+V)$ where $V$ satisfies a reverse H"older inequality. In that case the weights involved are a localized version of Muckenhoupt weights.