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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 interpolation in generalized Orlicz spaces
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by David Cruz-Uribe and Peter Hästö PDF
Trans. Amer. Math. Soc. 370 (2018), 4323-4349 Request permission


We prove versions of the Rubio de Francia extrapolation theorem in generalized Orlicz spaces. As a consequence, we obtain boundedness results for several classical operators as well as a Sobolev inequality in this setting. We also study complex interpolation in the same setting and use it to derive a compact embedding theorem. Our results include as special cases classical Lebesgue and Sobolev space estimates and their variable exponent and double phase growth analogs.
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Additional Information
  • David Cruz-Uribe
  • Affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487-0350
  • MR Author ID: 329597
  • Email:
  • Peter Hästö
  • Affiliation: Department of Mathematical Sciences, P.O. Box 3000, FI-90014 University of Oulu, Finland – and – Department of Mathematics and Statistics, FI-20014 University of Turku, Finland
  • Email:
  • Received by editor(s): July 25, 2016
  • Received by editor(s) in revised form: December 5, 2016
  • Published electronically: February 21, 2018
  • Additional Notes: The first author was supported by NSF grant DMS-1362425 and research funds from the Dean of the College of Arts & Sciences, the University of Alabama
    The authors would also like to thank the anonymous referee for several useful comments and additional references
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 4323-4349
  • MSC (2010): Primary 46E35; Secondary 46E30, 42B20, 42B25
  • DOI:
  • MathSciNet review: 3811530