Extrapolation and weighted norm inequalities in the variable Lebesgue spaces

Abstract

We extend the theory of Rubio de Francia extrapolation, including off-diagonal, limited range, and $A_{\infty }$ extrapolation, to the weighted variable Lebesgue spaces. As a consequence we are able to show that a number of different operators from harmonic analysis are bounded on these spaces. The proofs of our extrapolation results are developed in a way that outlines a general approach to proving extrapolation theorems on other Banach function spaces.

34 pages

References in corpus (1)

• Extensions of Rubio de Francia's extrapolation theorem in variable Lebesgue space and application