Hardy Operator Commutators Several Sector Results

The theory of Hardy operators is one of the very important operators in harmonic analysis, and recently it becomes the focus of more and more experts. In this paper, firstly, the basic knowledge and theories of Hardy operators are introduced, by using the research methods or skills of real harmonic analysis and the properties of the weighted Ai functions, the boundedness for the commuta-tors of fractional Hardy operators in weighted homogeneous Morrey-Herz spaces is obtained. On this basis, we introduce the multilinear commutators and prove the boundedness for the multilinear commutators of fractional Hardy operators in weighted homogeneous Morrey-Herz spaces, finally,λ-central BMO spaces and A-central Morrey spaces are introduced,then, we discussλ-central BMO estimates for multilinear commutators of fractional Hardy operators. These re-sults supplement the theory of Hardy operators, and expand the boundedness results on Morrey spaces.