齊次 Morrey-Herz 空間上廣義 Riesz 變換及其交換子的有界性

楊明華，許明，楊曉轉

（暨南大學數學系，廣東 廣州 510632

齊次 Morrey-Herz 空間上廣義 Riesz 變換及其交換子的有界性

楊明華，許明，楊曉轉

（暨南大學數學系，廣東 廣州 510632

1 引言

2 預備知識

3 主要結果及其證明

4 補充說明

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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(?n)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.

國家自然科學基金(10771221)；暨南大學青年自然科學基金(51208036).

楊明華(1986-)，碩士生，研究方向：調和分析.

2010 MSC:42B25