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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Extrapolation and weighted norm inequalities in the variable Lebesgue spaces

Authors: SFO David Cruz-Uribe and Li-An Daniel Wang
Journal: Trans. Amer. Math. Soc. 369 (2017), 1205-1235
MSC (2010): Primary 42B25, 42B35
Published electronically: April 8, 2016
MathSciNet review: 3572271
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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 $L^{p(\cdot )}(w)$. 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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Additional Information

SFO David Cruz-Uribe
Affiliation: Department of Mathematics, Trinity College, Hartford, Connecticut 06106
Address at time of publication: Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487

Li-An Daniel Wang
Affiliation: Department of Mathematics and Statistics, Sam Houston State University, Huntsville, Texas 77341
MR Author ID: 1015472

Keywords: Variable Lebesgue spaces, weights, Muckenhoupt weights, maximal operator, singular integrals, fractional integrals, Rubio de Francia extrapolation
Received by editor(s): August 19, 2014
Received by editor(s) in revised form: March 26, 2015
Published electronically: April 8, 2016
Additional Notes: Both authors were supported by the Stewart-Dorwart faculty development fund at Trinity College, and the first author was also supported by NSF grant 1362425
Article copyright: © Copyright 2016 American Mathematical Society