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arXiv · 1309.6063

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

Verónica Dimant·Pablo Sevilla-Peris
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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.

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Verónica Dimant, Pablo Sevilla-Peris. 2013-09-24. Summation of coefficients of polynomials on $\ell_{p}$ spaces. https://doi.org/10.5565/publmat-60216-02

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