University of Oulu

Cruz-Uribe, D., & Hästö, P. (2018). Extrapolation and interpolation in generalized Orlicz spaces. Transactions of the American Mathematical Society, 370(6), 4323–4349.

Extrapolation and interpolation in generalized Orlicz spaces

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Author: Cruz-Uribe, David1; Hästö, Peter2,3
Organizations: 1Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487-0350
2Department of Mathematical Sciences, P.O. Box 3000, FI-90014, University of Oulu, Finland
3Department of Mathematics and Statistics, FI-20014, University of Turku, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
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Language: English
Published: American Mathematical Society, 2018
Publish Date: 2019-05-23


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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Series: Transactions of the American Mathematical Society
ISSN: 0002-9947
ISSN-E: 1088-6850
ISSN-L: 0002-9947
Volume: 370
Issue: 6
Pages: 4323 - 4349
DOI: 10.1090/tran/7155
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: 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.
Copyright information: © 2018 American Mathematical Society. This is a post-peer-review, pre-copyedit version of an article published in Transactions of the American Mathematical Society Vol. 370 No. 6. The final authenticated version is available online at: