REMARKS ON THE LOCAL HOPFS LEMMA

The paper deals with the problem of extending the recent work of M.S.B aouendi and L.P.Rothschild concerning harmonic functions vanishing to infinite order in the normal direction in balls and half-spaces. Contr ary to what one expects, we show that the B.-R. result extends neither to arbitrary domains nor to cases when the normal is replaced by a cu rve transversal to the boundary. The exact criterion when the result h olds in R(2) is given.