 The lower bound is the analog in CR Geometry of the André Lichnerowicz bound for the first positive eigenvalue of the Laplace–Beltrami operator for compact manifolds in Riemannian geometry.Non-negativity of the CR Paneitz operator in dimension 3 is a CR invariant condition as follows by the conformal covariant properties of the CR Paneitz operator on CR manifolds of real dimension 3, first observed by Kengo Hirachi.The CR version of the Paneitz operator, the so-called CR Paneitz Operator first appears in a work of C. Robin Graham and Jack Lee.