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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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