梅蒂维尔不等式和超微分低椭球性

Pub Date : 2024-02-28 DOI:10.1002/mana.202300147

Paulo D. Cordaro, Stefan Fürdös

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引用次数: 0

摘要

1980 年，Métivier 通过先验估计描述了可解偏线性微分算子的解析（和 Gevrey）次椭圆性。在本论文中，我们将这一特征扩展到由适当权重序列给出的 Denjoy-Carleman 类的超微分低椭圆性。我们还讨论了解可以作为超函数的情况，并介绍了一些应用。

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The Metivier inequality and ultradifferentiable hypoellipticity

In 1980, Métivier 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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