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Extrapolation and interpolation in generalized Orlicz spaces


Authors: David Cruz-Uribe and Peter Hästö
Journal: Trans. Amer. Math. Soc. 370 (2018), 4323-4349
MSC (2010): Primary 46E35; Secondary 46E30, 42B20, 42B25
DOI: https://doi.org/10.1090/tran/7155
Published electronically: February 21, 2018
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Abstract: 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
Email: dcruzuribe@ua.edu

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: peter.hasto@oulu.fi

DOI: https://doi.org/10.1090/tran/7155
Keywords: Non-standard growth, variable exponent, Musielak--Orlicz spaces, extrapolation, weighted norm inequalities
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
Article copyright: © Copyright 2018 American Mathematical Society

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