齐次 Morrey-Herz 空间上广义 Riesz 变换及其交换子的有界性

杨明华，许明，杨晓转

（暨南大学数学系，广东 广州 510632

齐次 Morrey-Herz 空间上广义 Riesz 变换及其交换子的有界性

杨明华，许明，杨晓转

（暨南大学数学系，广东 广州 510632

1 引言

2 预备知识

3 主要结果及其证明

4 补充说明

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Boundedness of generalized Riesz transform and its commutator on the homogeneous Morrey-Herz spaces

Yang Minghua,Xu Ming,Yang Xiaozhuan

(Department of Mathematics,Ji′nan University,Guangzhou 510632,China)

In this paper,we study the generalized Riesz transform∇L-1/2associated with divergence form elliptic operator and its commutator[b,∇L-1/2]generated by generalized Riesz transform and BMO(Rn)functions.By them ethods of studying ring decom position of function and thier corresponding truncated operators, their boundedness of the results form space MKα,λp1,q(Rn)to space MKα,λp2,q(ℝn)were established.The well-known results gotten by before scholars are extended.

ellip tic operator,commutator,homogeneous Morrey-Herz,Riesz transform,BMO(Rn)

2011-09-17.

国家自然科学基金(10771221)；暨南大学青年自然科学基金(51208036).

杨明华(1986-)，硕士生，研究方向：调和分析.

2010 MSC:42B25