齐次Morrey—Herz空间上广义Riesz变换及其交换子的有界性

摘要

主要研究与二阶散度型椭圆算子L相伴的Riesz变换△↓L^-1／2及其与BMO（R^n）函数生成的交换子，采用对函数进行环形分解的技术和对算子转化为相应的截断算子的方法，得出它们从MKp1,q^α,λ（R^n）到MKp2,q^α,λ（R^n）是有界的，从而推广了以前学者的结论．%In this paper, we study the generalized Riesz transform △↓L^-1/2 associated with divergence form elliptic operator and its commutator [b, △↓L^-1/2] generated by generalized Riesz transform and BMO（R^n） functions. By the methods of studying ring decomposition of function and thier corresponding truncated operators, their boundedness of the results form space MKp1,q^α,λ（R^n） to space MKp2,q^α,λ（R^n ） were established. The well-known results gotten by before scholars are extended.