This is an announcement for the paper "Absolutely summing multilinear operators via interpolation" by N. Albuquerque, D. Nunez-Alarcon, J. Santos and D. M. Serrano-Rodriguez.

Abstract: We use an interpolative technique from \cite{abps} to introduce the notion of multiple $N$-separately summing operators. Our approach extends and unifies some recent results; for instance we recover the best known estimates of the multilinear Bohnenblust-Hille constants due to F. Bayart, D. Pellegrino and J. Seoane-Sep'ulveda. More precisely, as a consequence of our main result, for $1\leq t<2$ and $m\in \mathbb{N}$ we prove that $$ \left( \sum_{i_{1},\dots ,i_{m}=1}^{\infty }\left\vert U\left(e_{i_{1}},\dots ,e_{i_{m}}\right) \right\vert^{\frac{2tm}{2+(m-1)t}}\right)^{\frac{2+(m-1)t}{2tm}} \leq \left[\prod_{j=2}^{m}\Gamma \left( 2-\frac{2-t}{jt-2t+2}\right) ^{\frac{t(j-2)+2}{2t-2jt}}\right] \left\Vert U\right\Vert $$ for all complex $m$-linear forms $U:c_{0}\times \cdot \cdot \cdot \times c_{0}\rightarrow \mathbb{C}$.

Archive classification: math.FA

Submitted from: ngalbqrq@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1404.4949

or

http://arXiv.org/abs/1404.4949