  We describe a set of conformally covariant boundary operators associated to
the Paneitz operator, in the sense that they give rise to a conformally
covariant energy functional for the Paneitz operator on a compact Riemannian
manifold with boundary. These operators naturally give rise to a first- and
third-order conformally covariant pseudodifferential operator. In the setting
of Poincar\'e--Einstein manifolds, we show that these operators agree with the
fractional GJMS operators of Graham and Zworski. We also use our operators to
establish some new sharp Sobolev trace inequalities.
