Weighted Sobolev type inequalities in a smooth metric measure space. (English) Zbl 1532.53067
Summary: In this paper, we obtain weighted Sobolev type inequalities with explicit constants that extend the inequalities obtained by Q. Guo et al. [Math. Res. Lett. 28, No. 5, 1419–1439 (2021; Zbl 1498.53054)] in the Riemannian setting. As an application, we prove some new logarithmic Sobolev type inequalities in some smooth metric measure spaces.
MSC:
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 53C23 | Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces |
| 58J32 | Boundary value problems on manifolds |
Citations:
Zbl 1498.53054References:
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