Extrapolation and interpolation in generalized Orlicz spaces

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...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2018-06, Vol.370 (6), p.4323-4349
Main Authors: David Cruz-Uribe, Peter Hästö
Format: Article
Language:English
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Summary: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/7155