Comparison theorems for GJMS operators

In this paper, we compare the first order fractional GJMS (see Graham et al. (1992)) operator P1 with the conformal Laplacian P2, on the conformal infinity of a Poincare-Einstein manifold. We derive some inequalities between the Yamabe constants and the first eigenvalues associated with P1 and P2, and prove some rigidity theorems by characterizing the equalities. Similarly, some comparison theorems between P2 and the Paneitz operator P4 or the 6th order GJMS operator P6 are also given.