Research On The Bounded Properties Of Operators On Two Types Of Morrey Spaces

In this thesis,we mainly analyse the problem of operator inequalities of Morrey spaces associated with Karamata regular variation.And we also introduce the relation between central Morrey spaces,Herz spaces and Morrey-Herz spaces with variable exponent.For an applications,We will establish the boundedness for the homogeneous fractional integral operator TΩ,σ and its commutator[b,TΩ,σ]on the Morrey-Herz space with variable exponent.The main contents of the thesis consist of four chapters:The first chapter includes three parts,in the first paxt,we introduce the origin and basic definition of morrey space.In the second part,we give the research definition of weight function(w∈ Ap)and its properties.In the third and fourth parts,we introduce the definitions and the existing research results of weighted Morrey spaces and one-sided operators,respectively.In the fifth part,we introduce the boundedness of one-sided operator on Morrey space which associated with Karamata regular variation.In the sixth part,the work of this thesis is briefly introduced.In the second chapter,one-sided operator on Morrey space associated with Karama-ta regular variation axe considered.There are three parts in this chapter.In the first part,we present a few related lemmas.In the next part,We studied the boundedness of one-sided operator on one-dimensional Morrey space associated with.Karamata regular vari-ation.Finally,the boundedness of operators on n-dimensional Morrey space associated with Karamata regular variation are considered.In chapters three,we will give the relation between central Morrey spaces,Herz spaces and Morrey-Herz spaces with variable exponent.For an applications,We will establish the boundedness for the homogeneous fractional integral operator TΩ,σ and its commutator[b,TΩ,σ]on the Morrey-Herz space with variable exponent.In the last chapter,we summarize the main work of the thesis,and give some suggestions and expectations to the research in future.