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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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