A strong unique continuation result for the Baouendi operator

Abstract

We establish a strong unique continuation property for the subelliptic Baouendi operator under the presence of zero-order perturbations satisfying an almost Hardy-type growth condition. In particular, the admissible class includes both $L_{\mathrm{loc}}^{\infty }$ and singular potentials. We prove that any solution vanishing to infinite order at a point of the degeneracy manifold of the operator must be identically zero. The result holds extends to variable-coefficient operators with intrinsic Lipschitz regularity. A notable feature of the proof is that it relies exclusively on $L^2$ Carleman estimates combined with the classical Hardy inequality.