Luis Miguel Castaño Marín

Optimality in a Multilinear Extension of Kwapie\'n's Theorem

Bayart, Pellegrino and Rueda proved that every continuous $m$-linear operator from $(\ell_1)^m$ into $\ell_p$ is absolutely $(r_{m,p};1)$-summing, for explicit exponents $r_{m,p}$. The optimality of these exponents was known for $2\le p\le\infty$. We prove optimality in the remaining range $1\le p<2$. Our argument is f...