CARLEMAN ESTIMATES FOR A SUBELLIPTIC OPERATOR AND UNIQUE CONTINUATION

We establish a Carleman type inequality for the subelliptic operator L = DELTA(z) + Absolute value of x 2partial derivative(t)2 in R(n+1), n greater-than-or-equal-to 2, where z is-an-element-of R(n), t is-an-element-of R. As a consequence, we show that -L + V has the strong unique continuation property at points of the degeneracy manifold {(0, t) is-an-element-of R(n+1)\t is-an-element-of R} if the potential V is locally in certain L(p) spaces.