Abstract
CR invariant differential operators on densities with leading part a power of the sub-Laplacian are derived. One family of such operators is constructed from the ‘‘conformally invariant powers of the Laplacian’’ via the Fefferman metric; the powers which arise for these operators are bounded in terms of the dimension. A second family is derived from a CR tractor calculus which is developed here; this family includes operators for every positive power of the sub-Laplacian. This result together with work of Čap, Slovák and Souček imply in three dimensions the existence of a curved analogue of each such operator in flat space.
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