ω-hypoelliptic differential operators of constant strength

We study ω-hypoelliptic differential operators of constant strength. We show that any operator with constant strength and coefficients in Eω(Ω) which is homogeneous ω-hypoelliptic is also σ -hypoelliptic for any weight function σ = O(ω). 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 (ω, σ ) to conclude that, for any operator P(x,D) with constant strength, the σ -hypoellipticity of the frozen operator P(x0,D) implies the ω-hypoellipticity of P(x,D). This requires the use of pseudodifferential operators.  2004 Elsevier Inc. All rights reserved