卷积型算子非局部热核的逐点估计
Point-wise estimates for nonlocal heat kernel of convolution type operators
摘要：
本文讨论了一类非局部卷积型算子的热核的逐点估计，该算子的热核在无穷远处至少指数衰减。结果表明，热核的大时间行为基本上取决于是否$|x|\ll t$，或$|x|\sim t$，或$|x|\gg t$。我们得到尖锐的逐点上界的热核在所有这些地区。在第一个区域的非局部热核的行为像经典的，而在其他地区，我们观察到一个本质的区别。
英文摘要：
The paper deals with point-wise estimates for the heat kernel of a nonlocal convolution type operator with a kernel that decays at least exponentially at infinity. It is shown that the large time behaviour of the heat kernel depends essentially on whether $|x|\ll t$, or $|x|\sim t$, or $|x|\gg t$. We obtain sharp point-wise upper bounds for the heat kernel in all these regions. In the first region the nonlocal heat kernel behaves like the classical one, while in the other regions we observe an essential difference.
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