A factorization of the GJMS operators of special Einstein products and applications

We show that the GJMS operators of a special Einstein product factor as a composition of second- and fourth-order differential operators. In particular, our formula applies to the Riemannian product (Formula presented.). We also show that there is an integer (Formula presented.) such that if (Formula presented.), then for any special Einstein product (Formula presented.), the Green's function for the GJMS operator of order (Formula presented.) is positive. As a result, these products give new examples of closed Riemannian manifolds for which the (Formula presented.) -Yamabe problem is solvable.