Extrapolation and interpolation in generalized Orlicz spaces



: David Cruz-Uribe, Peter Hästö

Publisher: AMER MATHEMATICAL SOC

: 2018

: Transactions of the American Mathematical Society

: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

: T AM MATH SOC

: 370

: 6

: 4323

: 4349

: 27

: 0002-9947

DOI: https://doi.org/10.1090/tran/7155

: https://research.utu.fi/converis/portal/detail/Publication/31020732


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.

Last updated on 2024-26-11 at 22:45