ELLIPTICITY, HYPOELLIPTICITY AND PARTIAL HYPOELLIPTICITY OF DIFFERENTIAL OPERATORS

The conditions for ellipticity and hypoellipticity of operator P ( D ) in terms of fundamental solutions were described by HÄormander [2]. But the relationship and the difference of condition of ellipticity, hypoellipticity and partial hypoellipticity of operator P ( D ) in terms of fundamental solutions was not established. W e look at the case when the solution u of the equation P ( D ) u = f is conditionally smooth whenever f is a smooth function.