arXiv 2202.045232022-02-09math.FA

Unified Grothendieck's and Kwapień's theorems for multilinear operators

Daniel Núñez-Alarcón, Joedson Santos, Diana Serrano-Rodríguez

备注：: 10 pages

英文摘要：

Kwapień's theorem asserts that every continuous linear operator from $\ell_{1}$ to $\ell_{p}$ is absolutely $\left( r,1\right) $-summing for $1/r=1-\left\vert 1/p-1/2\right\vert .$ When $p=2$ it recovers the famous Grothendieck's theorem. In this paper investigate multilinear variants of these theorems and related issues. Among other results we present a unified version of Kwapień's and Grothendieck's results that encompasses the cases of multiple summing and absolutely summing multilinear operators.

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