Integral operators on the product of C(K) spaces

We study and characterize the integral multilinear operators on a product o f C(K) spaces in terms of the representing polymeasure of the operator. Som e applications are given. In particular, we characterize the Borel polymeas ures that can be extended to a measure in the product sigma -algebra, gener alizing previous results for bimeasures. We also give necessary conditions for the weak compactness of the extension of an integral multilinear operat or on a product of C(K) spaces. (C) 2001 Elsevier Science.