Morrey Meets Herz with Variable Exponent and Applications to Commutators of Homogeneous Fractional Integrals with Rough Kernels

摘要

We define the new centralMorrey space with variable exponent and investigate its relation to theMorrey-Herz spaces with variable exponent. As applications, we obtain the boundedness of the homogeneous fractional integral operator T_(Ω,σ) and its commutator [b, T_(Ω,σ)] on Morrey-Herz space with variable exponent, where Ω ∈ L~s(S~(n-1)) for s ≥ 1 is a homogeneous function of degree zero, 0 < σ < n, and b is a BMO function.