Extrapolation and interpolation in generalized Orlicz spaces

Cruz-Uribe, David; Hästö, Peter (2018-06-30)
 
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https://doi.org/10.1090/tran/7155

Cruz-Uribe, David
Hästö, Peter
American Mathematical Society
30.06.2018

Cruz-Uribe, D., & Hästö, P. (2018). Extrapolation and interpolation in generalized Orlicz spaces. Transactions of the American Mathematical Society, 370(6), 4323–4349. https://doi.org/10.1090/tran/7155

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© 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: https://doi.org/10.1090/tran/7155.
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doi:https://doi.org/10.1090/tran/7155
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https://urn.fi/URN:NBN:fi-fe2019052316715
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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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