| The boundedness of Hardy operator in all kinds of spaces is one of the important contents in harmonic analysis.It plays an important role in the fields of probability theory.At the same time,Hardy operator with rough kernel is very important,which attracts the interest of mathematics workers.Therefore,Hardy operator with rough kernel becomes the research object of this dissertation.In this paper,we study the boundedness of bilinear Hardy operator commutators with rough kernel in λ-central Morrey spaces and the boundedness of single linear Hardy operator commutators with rough kernel in homogeneous weighted Herz spaces,the main conclusions are as followsIn the first part,the boundedness of bilinear Hardy operator commutators with rough kernel in λ-central Morrey spaces is investigated.Firstly,according to the definitions ofλ-central Campanato spaces and bilinear Hardy operators with rough kernel,the commutators generated by the λ-central Campanato space and the bilinear Hardy operators with rough kernels are studied.Secondly,in order to deal with bilinear,based on Holder inequality,the bilinear Hardy operator commutator is decomposed.Finally,By analysis,it is proved that the bilinear Hardy operator commutator with rough kernel is bounded in λ-central Morrey space.In the second part,the boundedness of n dimensional Hardy operator commutators with rough kernel in homogeneous weighted Herz spaces is proved.Firstly,a class of weighted central BMO spaces is introduced,and n dimensional Hardy operator commutators with rough kernel are defined.Secondly,the homogeneous weighted Herz space is introduced.Finally,by using the related properties of weight function classes and some basic theories and methods in harmonic analysis,the weighted boundedness of commutators of this kind of Hardy operator in homogeneous weighted Herz space is proved. |
