Boundedness of Commutators Generated by the Rough Fractional Maximal Operator on Variable Exponent Central Morrey Spaces

In this paper, using harmonic analysis tools−including spherical harmonic decomposition of kernels, sharp maximal function estimates, and variable exponent space theory—we investigate the boundedness of the commutator [b,MΩ,β] on variable exponent central Morrey spaces, under suitable regularity conditions on the variable exponents. Here, Ω∈Ll(Sn−1) (l≥1) denotes a zero-degree homogeneous function on the unit sphere Sn−1, β satisfies 0≤β<n, and b∈CBMO(Rn).