The Properties Of Commutators On Homogeneous Herz-Morrey Spaces

In this dissertation,some boundedness of commutators on homogeneous Herz-Morrey spaces are established.A triple(X,d,μ)is called a space of homogeneous type,if X is a non-empty set,and d is a quasi-metric on X,along with a non-negative measureμsatisfyingμ(B(x,2r))≤Aμ(B(x,r))＜∞for any x∈X,r∈[0,∞),where B(x,r)= {y∈X|d(x,y)＜r},and A denotes a constant independent of r and x.In the first chapter,by the properties of spaces of homogeneous type(X,d,μ),we get the boundedness of the commutators associated with fractional integral operators and BMO(X)functions on the homogeneous Herz-Morrey space M(?)_p,q^α,λ(X)on spaces of homogeneous type.Let g_ψbe the Littlewood-Paley g function and g_ψ,bbe the commutator generated by Littlewood-Paley g function and BMO(Rⁿ)functions.In the second chapter,we consider the property of the operator g_ψon the homogeneous Herz-Morrey space M(?)_p,q^α,λ(Rⁿ),and get the boundedness of the commutator g_ψ,bon the same space.In the last chapter,based on the second chapter,we will study the bounded-ness of the operator g_ψand the commutator g_ψ,bon the weighted Herz-Morrey space M(?)_p,q^α,λ(ω₁,ω₂),whereω₁,ω₂ is A₁ weight..