Interpolation of multilinear operators acting between quasi-Banach spaces

Grafakos, L.; Mastyło, M.; Szwedek, R.

doi:10.1090/S0002-9939-2014-12083-1

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.

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