与可测系数二阶微分算子相连的分数次积分算子的加权估计

The weighted estimation of fractional integral operators with measurable coefficient and second order differential operators

主要研究了与二阶散度型椭圆算子L相关的分数次积分算子L-β/2的加权估计,假定椭圆算子L相伴的热核具有L2off-diagonal估计,利用对函数进行环形分解的技术以及将算子转化为相应的截断算子的方法,证明了该分数次积分算子从MKαp,,λq1(ω1,ωq12)到MKα,λp,q2(ω1,ωq22)是有界的.

Let L be elliptic operator, when the heat kernel associated to L has L2 off-diagonal estimation, the fractional integral operators L-β/2 associated with divergent elliptic operator has been investigated. It has been proved the boundedness from space MKαp,,λq1（ω1,ωq12） to space MKα,λp,q2（ω1,ωq22） by the methods of studying ring decomposition of functions and their corresponding truncated operators.