We build up a quantitative second-order Sobolev estimate of for positive -harmonic functions in Riemannian manifolds under Ricci curvature bounded from below and also for positive weighted -harmonic functions in weighted manifolds under the Bakry-Émery curvature-dimension condition.

中文翻译：

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曲率维数条件下流形中（加权）p调和函数的定量二阶估计

我们对下界里奇曲率下黎曼流形中的正调和函数以及 Bakry-Émery 曲率维数条件下加权流形中的正加权调和函数建立了定量二阶 Sobolev 估计。