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RESEARCH PRODUCT

ω-hypoelliptic differential operators of constant strength

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Abstract We study ω-hypoelliptic differential operators of constant strength. We show that any operator with constant strength and coefficients in E ω (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.