与微分算子相关的分数次积分算子交换子的有界性

Boundedness of the commutators of the fractional integral operators related to differential operators

摘要: 采用类似Plauszynski相应定理的证明方法以及环形分解的技巧,证明了与二阶散度型椭圆算子L相联系的分数次积分算子L-α2与Lipschitz函数b生成的交换子b,L-α2在Triebel-Lizorkin空间的有界性.

Abstract: The fractional integral operators L-α2 associated with divergence form elliptic operator is studied.By the methods similar to Plauszynski theory and ring decomposition of domains,the boundedness of commutators b,L-α2 with b belonging to Lipschitz funtions on the Triebel-Lizorkin spaces are obtained.