This is an announcement for the paper "Summation of coefficients of polynomials on $\ell_{p}$ spaces" by Veronica Dimant and Pablo Sevilla-Peris.

Abstract: We investigate the summability of the coefficients of $m$-homogeneous polynomials and $m$-linear mappings defined on $\ell_{p}$-spaces. In our research we obtain results on the summability of the coefficients of $m$-linear mappings defined on $\ell_{p_{1}} \times \cdots \times \ell_{p_{m}}$. The first results in this respect go back to Littlewood and Bohnenblust and Hille (for bilinear and $m$-linear forms on $c_{0}$) and Hardy and Littlewood and Praciano-Pereira (for bilinear and $m$-linear forms on arbitrary $\ell_{p}$-spaces). Our results recover and in some case complete these old results through a general approach on vector valued $m$-linear mappings.

Archive classification: math.FA

Submitted from: psevilla@mat.upv.es

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

http://front.math.ucdavis.edu/1309.6063

or

http://arXiv.org/abs/1309.6063