A new multilinear insight on Littlewood's 4/3-inequality

We unify Littlewood's classical 4/3-inequality (a forerunner of Grothendieck's inequality) together with its m-linear extension due to Bohnenblust and Hille (which originally settled Bohr's absolute convergence problem for Dirichlet series) with a scale of inequalties of Bennett and Carl in ℓp-spaces (which are of fundamental importance in the theory of eigenvalue distribution of power compact operators). As an application we give estimates for the monomial coefficients of homogeneous ℓp-valued polynomials on c0.