Summability of multilinear mappings: Littlewood, Orlicz and beyond

Oscar Blasco, Geraldo Botelho, Daniel Pellegrino, Pilar Rueda

Published 2008-10-12Version 1

In this paper we prove a plenty of new results concerning summabililty properties of multilinear mappings between Banach spaces, such as an extension of Littlewood's 4/3 Theorem. Among other features, it is shown that every continuous n-linear form on the disc algebra or the Hardy space is (1;2,...,2)-summing, the role of the Littlewood-Orlicz property in the theory is established and the interplay with almost summing multilinear mappings is explored.