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Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling
Bin Qian, Beibei Zhang · 2024-11-21 · via math.PR updates on arXiv.org

In this paper, we obtain the reverse Bakry-Émery type estimates for a class of hypoelliptic diffusion operator by coupling method. The (right and reverse) Poincaré inequalities and the (right and reverse) logarithmic Sobolev inequalities are presented as consequences of such estimates. Wang-Harnack inequality, Hamilton's gradient estimate and Liouville property are also presented by reverse logarithmic Sobolev inequality.

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