Hypoellipticity of second order differential operators

Abstract

We are concerned with the second order partial differential operators generated by the smooth real vector fields $X_0$, …, $X_k$. We extend a sufficient condition for the hypoellipticity of the operators of the form $ ∑_{j=0}^kX_j^2+X_0$ to that for the second order pseudodifferential operators of the form $ ∑_{j=1}^kA_j^2+iA_0+B$.