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We give conditions so that a polynomial be factorable throu- gh an Lr(µ) space. Among them, we prove that, given a Banach space X and an index m, every absolutely summing operator on X is 1-factorable if and only if every 1-dominated m-homogeneous polynomial on X is right 1-factorable, if and only if every 1-dominated m-homogeneous polynomial on X is left 1-factorable. As a consequence, if X has local unconditional structure, then every 1-dominated homogeneous polynomial on X is right and left 1-factorable.

POLYNOMIAL FACTORIZATION THROUGH Lγ(μ) SPACES

POLYNOMIAL FACTORIZATION THROUGH L_γ(μ) SPACES