A local version of Rubio de Francia's extrapolation theorem (Q1277651)

The author studies operators on weighted \(L^p\) spaces of the form \(L^p(\mathbb{R}^n,wdx)\) where \(w\) is a given weight function. Drawing on some results due to \textit{J. Alvarez}, \textit{R. J. Bagby}, \textit{D. S. Kurtz} and \textit{C. Pérez} [Stud. Math. 104, No. 2, 195-209 (1993; Zbl 0809.42006)], she shows that if an operator \(T\) is bounded on \(L^p(\mathbb{R}^n, wdx)\) for a certain family of weight functions \(w\), then \(T\) is bounded on \(L^r(\mathbb{R}^n, dx)\) for a certain range of exponents \(r\) which contains \(p\).