Boundedness for a Class of Generalized Commutators of Fractional Hardy Operators with a Rough Kernel

Abstract EN

The authors consider the generalized commutator of fractional Hardy operator with a rough kernel as follows: ℋΩ,A,βmf(x)=1/(|x|n-β)∫|y|<|x|(Ω(x-y)/|x-y|m-1)Rm(A;x,y)f(y)dy, where Ω∈Lr(?n-1), 0≤β

The authors prove that ℋΩ,A,βm is bounded on Herz type space and λ-Central Morrey space with m≥1, which is an open problem for m>2.