论文标题
Sobolev和BV通过热核的短时行为在$ \ mathrm {rcd} $空间上发挥作用
Sobolev and BV functions on $\mathrm{RCD}$ spaces via the short-time behaviour of the heat kernel
论文作者
论文摘要
在有限维$ \ mathrm {rcd}（k，n）$空间的设置中，我们表征了$ p $ -sobolev空间的$ p \ in（1，\ infty）$的$ p \ and（1，\ infty）$和有界变化功能的空间。此外，我们证明，Cheeger $ p $ edragies和总变化可以计算为涉及热核的非本地功能的限制。
In the setting of finite-dimensional $\mathrm{RCD}(K,N)$ spaces, we characterize the $p$-Sobolev spaces for $p\in(1,\infty)$ and the space of functions of bounded variation in terms of the short-time behaviour of the heat flow. Moreover, we prove that Cheeger $p$-energies and total variations can be computed as limits of nonlocal functionals involving the heat kernel.
