Power concave operators and representation of p-convex and q-concave Banach lattices

[EN] As a consequence of the analysis of the class of (p, q)-power concave operators, we prove a general representation theorem for p-convex and q-concave Banach lattices as spaces of integrable functions with respect to vector measures. This result culminates a series of representation theorems for Banach lattices using vector measures that have been obtained in the last twenty years.