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
Extrapolation and interpolation in generalized Orlicz spaces
|Author:||Cruz-Uribe, David1; Hästö, Peter2,3|
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
|Online Access:||PDF Full Text (PDF, 0.3 MB)|
|Persistent link:|| http://urn.fi/urn:nbn:fi-fe2019052316715
American Mathematical Society,
|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.
Transactions of the American Mathematical Society
|Pages:||4323 - 4349|
|Type of Publication:||
A1 Journal article – refereed
|Field of Science:||
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.
© 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.