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Extrapolation and weighted norm inequalities in the variable Lebesgue spaces


Authors: David Cruz-Uribe, SFO and Li-An Daniel Wang
Journal: Trans. Amer. Math. Soc. 369 (2017), 1205-1235
MSC (2010): Primary 42B25, 42B35
DOI: https://doi.org/10.1090/tran/6730
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

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

Li-An Daniel Wang
Affiliation: Department of Mathematics and Statistics, Sam Houston State University, Huntsville, Texas 77341
Email: ldw@shsu.edu

DOI: https://doi.org/10.1090/tran/6730
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