Extrapolation and weighted norm inequalities in the variable Lebesgue spaces

David Cruz-Uribe, SFO; Wang, Li-An

doi:10.1090/tran/6730

Extrapolation and weighted norm inequalities in the variable Lebesgue spaces
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by SFO David Cruz-Uribe and Li-An Daniel Wang PDF

Trans. Amer. Math. Soc. 369 (2017), 1205-1235 Request permission

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 $L^{p(\cdot )}(w)$. 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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