Global Real Analyticity of the Kohn–Laplacian on Pseudoconvex CR Manifolds with Comparable Levi Form

Abstract

In this paper, we study the global analytic hypoellipticity of the \(\Box _b\) operator on a general CR manifold of real dimension \((2n-1)\), with \(n\ge 3\). In particular, if M is a compact, real analytic, pseudoconvex CR manifold satisfying the \(D^{\epsilon }(q)\) and \((CR-P_q)\) conditions, and a special property for vector field T, we consider the following nonelliptic partial differential equation $$\begin{aligned} \Box _bu=f. \end{aligned}$$ If f is globally real analytic, we conclude that u is globally real analytic as well. The methods applied in this work are inspired from Tartakoff (1(4):283–311, 1976) and Tartakoff (89–90:85–116 1981).