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In this paper we give a different interpretation of Bombieri's norm. This new point of view allows us to work on a problem posed by Beauzamy about the behavior of the sequence S n (P ) = sup Q n [P Q n ] 2 , where P is a fixed m−homogeneous polynomial and Q n runs over the unit ball of the Hilbert space of n−homogeneous polynomials. We also study the factor problem for homogeneous polynomials defined on C N and we obtain sharp inequalities whenever the number of factors is no greater than N .doi:10.1090/s0002-9947-2012-05403-1 fatcat:o6wv5yjb2zgjbewnhmlhsfhi4i