极大交换子在各向异性空间的有界性

【作者】 张荣欣；

【导师】 赵凯；

【作者基本信息】 青岛大学 ， 应用数学， 2008， 硕士

【摘要】 本文介绍了各向异性Hardy空间和有关Hardy型空间的基础知识及理论，简单阐述了这些空间的最新进展．受齐次Morrey-Herz型函数空间的启发，引进了一类各向异性的齐次Morrey-Herz型函数空间，验证了此空间上常用的基本不等式及插值定理，并用内插法证明了各向异性空间上的Hardy-Littlewood极大交换子在L~p(R~n)空间上的有界性．由L~p(R~n)空间有界性结论，并利用Hardy-Littlewood极大交换子的性质，以及一些不等式估计，得到了Hardy-Littlewood极大交换子在各向异性的齐次Morrey-Herz型空间上的有界性结果．对于分数次极大交换子，在各向异性的齐次Morrey-Herz型空间上类似的有界性问题也得到了证明．最后还证明了满足一定尺寸条件的一类线性算子的交换子在各向异性的齐次Morrey-Herz型空间上的有界性．更多还原

【Abstract】 In this thesis, we recall some basic knowledge and theorems of anisotropic Hardy space and Herz type Hardy spaces, and describe the development of these sapces briefly. Motivated by the theory of homogeneous Morrey-Herz type spaces, a class of anisotropic homogeneous Morrey-Herz type spaces associated with a non-isotropic dilation A on R~n are introduced , some basic inequalities and interpolation theorems are established. By the interpolation theorems, the L~p boundedness of the commutator of Hardy-Littlewood maximal founction on anisotropic spaces are obtained. Using the L~p boundedness and the properties of the Hardy-Littlewood maximal fountions, the boundedness of the commutator of Hardy-Littlewood maximal founction on the homogeneous anisotropic Morrey-Herz type spaces can be proved. The same results are hold for the commutator of fractional maximal founction. Finally, we obtain the boundedness of the commutator of a class of linear operators which satisfied some size conditions.更多还原