ω-hypoelliptic differential operators of constant strength

We study omega-hypoelliptic differential operators of constant strength. We show that any operator with constant strength and coefficients in epsilon(omega)(Omega) which is homogeneous omega-hypoelliptic is also sigma-hypoelliptic for any weight function sigma=O(omega). We also present a sufficient condition in order to ensure that a differential operator admits a parametrix and, as a consequence, we obtain some conditions on the weights (omega, sigma) to conclude that, for any operator P(x, D) with constant strength, the sigma-hypoellipticity of the frozen operator P (x(0), D) implies the omega-hypoellipticity of P (x, D). This requires the use of pseudodifferential operators. (C) 2004 Elsevier Inc. All rights reserved.