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arXiv · 2303.14507

The Metivier inequality and ultradifferentiable hypoellipticity

Paulo D. Cordaro·Stefan Fürdös
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Abstract

In 1980 M{\'e}tivier characterized the analytic (and Gevrey) hypoellipticity of $L^2$-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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Paulo D. Cordaro, Stefan Fürdös. 2023-03-25. The Metivier inequality and ultradifferentiable hypoellipticity. https://doi.org/10.1002/mana.202300147

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