对称马氏过程梯度型算子弱(1,1)有界性的注记

Remarks on Weak Type(1,1) Boundedness of Gradient-Type Operator Associated with Symmetric Markov Processes

在假设热核估计满足一定的有界性条件下,讨论度量测度空间上对称马氏过程对应梯度型算子的弱(1,1)有界性,所得结论对建立马氏算子Riesz变换的有界性具有重要意义。最后通过相关例证说明所给假设条件的合理与普适性。

Under certain bounded condition on the heat kernel estimate, weak type(1,1)boundedness of gradient-type operator associated with symmetric Markov processes on metric measure space was discussed in this paper.This assertion is of great significance to establish the boundedness of Riesz transformation for Markov operators. Moreover,the rationality and universality of the given assumptions are illustrated by relevant examples.