Hypoellipticity of Some Degenerate Subelliptic Operators

The purpose of this paper is to establish the following result. LetL1andL2be subelliptic operators on Rnxand Rmy, respectively. Assume thatλ∈C∞(Rnx) withλ⩾0, assume thatλhas a zero of infinite order at the origin and that all other zeroes ofλare of finite order. Then the operatorL=L1+λL2is hypoelliptic.