A Functional Equation of Bohnemblust and Positive Homogeneous Functionals

We give a new version of a theorem proved by Bohnenblust and we deduce from it, in a direct way from a common background, several questions over characterization of positive homogeneous functionals. Some of them generalize earlier proved results related to L p-norms. Also we obtain a result related to the equality in the H¨older inequality.