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.

arXiv comment34 pages

References in corpus (4)

• Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights
• Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part III: Harmonic analysis of elliptic operators
• Greedy bases in variable Lebesgue spaces
• Extensions of Rubio de Francia's extrapolation theorem in variable Lebesgue space and application

Cited by in corpus (1)

• Greedy bases in variable Lebesgue spaces