Weighted Estimates For Multilinear Hausdorff Operators On Herz Spaces

There are four chapters in this dissertation,which study boundeness problem for some high dimensional Hausdorff operators on weighted Morrey-Herz spaces and weight-ed Herz-type Hardy space.The operators which we consider Hausdorff operators and Multilinear Hausdorff operators.In the first chapter,the author introduces the research background of Hausdorf-f operators and Multilinear Hausdorff operators,the development process of weighted Morrey-Herz spaces and weighted Herz-type Hardy space,and introduces the main re-search achievements.In the second chapter,The author introduces definition and related knowledge of weighted Morrey-Herz spaces,mainly use Holder inequality,polar decomposition and Minkowski inequality to get the sufficient condition for two kinds of high dimensional Hausdorff operators on this spaces.In the third chapter,The author introduces definition and related knowledge of weighted Herz-type Hardy space,mainly use the atomic decomposition of the homoge-neous weighted Herz-type Hardy space to get the sufficient condition for high dimensional Hausdorff operators on this spaces.In the fourth chapter,The author utilizes the same method and techniques of the second chapter to discuss the sufficient condition for three kinds of Multilinear Hausdorff operators on weighted Morrey-Herz spaces.