## Interpolation of multilinear operators acting between quasi-Banach spaces

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- by L. Grafakos, M. Mastyło and R. Szwedek PDF
- Proc. Amer. Math. Soc.
**142**(2014), 2507-2516 Request permission

## Abstract:

We show that interpolation of multilinear operators can be lifted to multilinear operators from spaces generated by the minimal methods to spaces generated by the maximal methods of interpolation defined on a class of couples of compatible $p$ -Banach spaces. We also prove the multilinear interpolation theorem for operators on Calderón-Lozanovskii spaces between $L_p$-spaces with $0< p \leq 1$. As an application we obtain interpolation theorems for multilinear operators on quasi-Banach Orlicz spaces.## References

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## Additional Information

**L. Grafakos**- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
- MR Author ID: 288678
- ORCID: 0000-0001-7094-9201
- Email: grafakosl@missouri.edu
**M. Mastyło**- Affiliation: Faculty of Mathematics and Computer Science, A. Mickiewicz University; and Institute of Mathematics, Polish Academy of Science (Poznań branch), Umultowska 87, 61-614 Poznań, Poland
- MR Author ID: 121145
- Email: mastylo@math.amu.edu.pl
**R. Szwedek**- Affiliation: Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
- Email: szwedek@amu.edu.pl
- Received by editor(s): August 16, 2012
- Published electronically: April 8, 2014
- Additional Notes: The first author was supported by the NSF grant DMS 0900946.

The second author was supported by the National Science Centre (NCN), Poland, grant No. 2011/01/B/ST1/06243. - Communicated by: Alexander Iosevich
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**142**(2014), 2507-2516 - MSC (2010): Primary 46B70, 46M35
- DOI: https://doi.org/10.1090/S0002-9939-2014-12083-1
- MathSciNet review: 3195771