对称马氏过程对应梯度型算子的弱(1,1)有界性

Weak Type(1,1)Boundedness of Gradient-type OperatorsAssociated with Symmetric Markov Process

考虑度量测度空间上对称马氏过程,并定义其对应的梯度型算子.在假设热核估计满足较弱的有界性条件下,建立该梯度型算子的弱(1,1)有界性.该结果对建立马氏算子Riesz变换的有界性有重要作用,可覆盖局部与非局部狄氏型框架.

The symmetric Markov process on metric space was considered,and the corresponding gradient operator was defined.Under the assumption that the thermonuclear estimation satisfied weak boundedness,the weak(1,1)boundedness of the gradient operator was established.This result played an important role in establishing the boundedness of the Riesz transform of Markov operators,which could be used to cover the local and non-local Dirichlet frames.