We discuss conformally covariant differential operators, which under local rescalings of the metric, δσg μν = 2σg , transform according to δσ∆ = r∆σ+(s−r)σ∆ for some r if ∆ is s th order. It is shown that the flat space restrictions of their associated Green functions have forms which are strongly constrained by flat space conformal invariance. The same applies to the variation of the Green fun...