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Interpolation of multilinear operators acting between quasi-Banach spaces


Authors: L. Grafakos, M. Mastyło and R. Szwedek
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
Published electronically: April 8, 2014
MathSciNet review: 3195771
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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.


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Additional Information

L. Grafakos
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
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
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

DOI: https://doi.org/10.1090/S0002-9939-2014-12083-1
Keywords: Interpolation spaces, quasi-Banach spaces, multilinear operators, functor Calder\'on-Lozanovskii spaces, Orlicz spaces.
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
Article copyright: © Copyright 2014 American Mathematical Society