Summation of coefficients of polynomials on Lp spaces

We investigate the summability of the coefficients of m-homogeneous polynomials and m-linear mappings defined on `p spaces. In our research we obtain results on the summability of the coefficients of m-linear mappings defined on Lp1 x ... x Lpm. The first results in this respect go back to Littlewood [17] and Bohnenblust and Hille [6] for bilinear and m-linear forms on c0, and Hardy and Littlewood [15] and Praciano-Pereira [20] for bilinear and m-linear forms on arbitrary `p spaces. Our results recover and in some case complete these old results through a general approach on vector valued m-linear mappings