The Metivier inequality and ultradifferentiable hypoellipticity
Abstract
In 1980 M\'etivier characterized the analytic (and Gevrey) hypoellipticity of L2-solvable partial linear differential operators by a-priori estimates. In this note we extend this characterization to ultradifferentiable hypoellipticity with respect to Denjoy-Carleman classes given by suitable weight sequences. We also discuss the case when the solutions can be taken as hyperfunctions and present some applications.
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