Sharp L p Carleman estimates and unique continuation

We will present a unique continuation result for solutions of second order differential equations of real principal type P (x,D)u + V (x)u = 0 with critical potential V in Ln/2 (where n is the number of variables) across noncharacteristic pseudo-convex hypersurfaces. To obtain unique continuation we prove Lp Carleman estimates, this is achieved by constructing a parametrix for the operator conjugated by the Carleman exponential weight and investigating its Lp − Lp boundedness properties.