Sums of CR and projective dual CR functions (Q2671272)

If \(S\) is a smooth strongly \(\mathbb{C}\)-convex real hypersurface in complex projective space, that is, locally projectively equivalent to a strongly convex hypersurface, then \(S\) admits a projective dual CR structure. See (1.2) for the explicit definition. In this paper, the authors give a characterization of whether a smooth function on \(S\) can be decomposed as the sum of a CR function and a dual CR function. This can be viewed as the analogue of the problem of decomposing a function as a sum of a CR function and a conjugate-CR function, that is, characterizing boundary values of pluriharmonic functions. See Theorem A and Theorem B for explicit results.