The Exchange Of The Child In The Anisotropic Space Bounded

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.