论文标题
对称马尔可夫半群的热内核上限
Heat kernel upper bounds for symmetric Markov semigroups
论文作者
论文摘要
众所周知，对称迪里奇形式的NASH型不平等等于相关的对称对称的Markov Semigroups的对分子热核上限。在本文中，我们表明这两者都暗示（因此等同于）在某些轻度假设下的非对角热内核上限。我们的方法基于一种新的广义戴维斯的方法。我们的结果扩展了\ cite {cks}的NASH型不平等的{CKS}，并大大扩展了功率顺序的不等式，并且还扩展了在完整的非紧凑型歧管上的二阶差分运算符的\ cite {gri}的{gri}。
It is well known that Nash-type inequalities for symmetric Dirichlet forms are equivalent to on-diagonal heat kernel upper bounds for the associated symmetric Markov semigroups. In this paper, we show that both imply (and hence are equivalent to) off-diagonal heat kernel upper bounds under some mild assumptions. Our approach is based on a new generalized Davies' method. Our results extend that of \cite{CKS} for Nash-type inequalities with power order considerably and also extend that of \cite{Gri} for second order differential operators on a complete non-compact manifold.
