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arXiv · 2512.12646

Uniformity of Maximal Hypoellipticity on Graded Lie Groups: From Pointwise to Global

Shiqi Liu·Edward McDonald·Fedor Sukochev·Dmitriy Zanin
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Abstract

On graded Lie groups, we develop a mechanism that transfers the uniformity of maximal hypoellipcity from the frozen coefficients principal part of a differential operator to the full operator. Our approach brings the century-old "freeze-unfreeze" strategy into the hypoelliptic setting, and offers a transparent and flexible framework for lifting symbol-level hypoelliptic properties to global elliptic estimates, without relying on pseudodifferential calculus. In addition, we prove that symmetric operators of hypoelliptic type on a graded Lie group are self-adjoint.

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Shiqi Liu, Edward McDonald, Fedor Sukochev, Dmitriy Zanin. 2025-12-14. Uniformity of Maximal Hypoellipticity on Graded Lie Groups: From Pointwise to Global. https://arxiv.org/abs/2512.12646

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