The Boundedness Of Commutators Generated By Hardy Operators And CMO Functions On Homogeneous Morrey Type Spaces

In this paper, we study the boundedness of some commutators generatedby CMO functions and Hardy operators on homogeneous Morreytype spaces.At first, we discuss the boundedness of the commutators Hbf(x) andH*b (f)(x) on homogeneous Morrey spaces Mλp (Rn), (0 <λ< 1/p ), where(?)and(?)We obtain that the commutators Hbf(x) and H*b (f)(x) are bounded onMλp (Rn), where p > 1, 0 <λ< 1/p , b∈CMOmax(p,p' ).Second, we prove that the commutators Hab f(x) is bounded on homogeneousMorrey types spaces, where Hab satisfies the condition(?)It is generated by CMO functions and Hardy operators Haf(x), where(?)Then, we get Hab f(x) is bounded on Mλp (Rn), (0 <λ< 1/p ), where 1 < p0