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 Hℓ×Sd−ℓ$H^{\ell } \times S^{d-\ell }$. We also show that there is an integer D=D(k,ℓ)$D = D(k,\ell)$ such that if d⩾D$d \geqslant D$, then for any special Einstein product Nℓ×Md−ℓ$N^\ell \times M^{d-\ell }$, the Green's function for the GJMS operator of order 2k$2k$ is positive. As a result, these products give new examples of closed Riemannian manifolds for which the Q2k$Q_{2k}$‐Yamabe problem is solvable. [ABSTRACT FROM AUTHOR]