Boundedness Of Some Kinds Of Operators On Function Spaces

The reserach of the boundedness of the operators is one of the important topics in harmonic analysis. In this thesis, the boundedness of some kinds of operators on function spaces are considered. We first introduce backgrounds and related problems of these operators, then these problems are discussed separately.In the first chapter, we investigate the boundedness of Littlewood-Paley g_λ~* operator on weighted Herz-type Hardy spaces, by using the decomposition theorem of Herz-type Hardy space in the terms of atoms and molecules.In the second chapter, the parametric Marcinkiewicz integral operatorμ_Ω~ρon BMO space is considered, when theΩandρsatisfy some conditions. We show thatμ_Ω~ρis well defined almost every where on the BMO space, and it is also bouneded.In the last chapter, we give the boundedness properties of maximal operator on a kind of function spaceof type of Morrey, which is defined on a homogeneous space.