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arXiv · 1408.4499

Extrapolation and weighted norm inequalities in the variable Lebesgue spaces

David Cruz-Uribe·Li-An Daniel Wang
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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.

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David Cruz-Uribe, Li-An Daniel Wang. 2014-08-19. Extrapolation and weighted norm inequalities in the variable Lebesgue spaces. https://arxiv.org/abs/1408.4499

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