Summation of coefficients of polynomials on $\ell_{p}$ spaces

By Verónica Dimant, P. Sevilla-Peris. 2013

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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.

View Paper: https://www.semanticscholar.org/paper/4b05dc55e062850f0a11b87c010bcf5f6fff03d1