Two Types Of Operator Commutators On Herz-type Hardy Space Weighted Boundedness

Let[b,T]denote the commutator which is generated by BMO function b andθtype Calderón-Zygmund operator T.And g_ψ,b is the commutator generated by BMO function b and Littlewood-Paley operator g_ψ.In this thesis,with the help of the theory of atomic decomposition and molecular decomposition of Herz-type Hardy space,it is proved that[b,T]is bounded on weighted Herz-type Hardy space,and also obtain that Littlewood-Paley operatorg_ψand the commutator g_ψ,b are bounded on Herz-type Hardy space and weighted Herz-type Hardy space.In the first chapter,we introduce some defines and theories about Herz-type Hardy spaces and weighted Herz-type Hardy spaces,Littlewood-Paley operator, Calderón-Zygmund operator.We also introduce some theoties about atomic decomposition and molecular decomposition of Herz-type Hardy space and weighted Herz-type Hardy space.And some boundedness about these spaces and operators are described.In the second chapter,it is proved that the commutator[b.T]is bounded on weighted Herz-type Hardy space with the help of atomic decomposition and molecular decomposition of the weighted Herz-type Hardy space.In the last chapter,also by the atomic and molecular decompositions,the boundedness of the Littlewood-Paley operator g_ψand the commutator g_ψ,b on Herz-type Hardy spaces are obtained.And weighted forms are discussed too.