Integral Operators on the Product of C K Spaces1

We study and characterize the integral multilinear operators on a product of C K spaces in terms of the representing polymeasure of the operator. Some applications are given. In particular, we characterize the Borel polymeasures that can be extended to a measure in the product σ-algebra, generalizing previous results for bimeasures. We also give necessary conditions for the weak compactness of the extension of an integral multilinear operator on a product of C K spaces