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
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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.References
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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
- Email: dcruzuribe@ua.edu
- Li-An Daniel Wang
- Affiliation: Department of Mathematics and Statistics, Sam Houston State University, Huntsville, Texas 77341
- MR Author ID: 1015472
- Email: ldw@shsu.edu
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 1205-1235
- MSC (2010): Primary 42B25, 42B35
- DOI: https://doi.org/10.1090/tran/6730
- MathSciNet review: 3572271