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The authors prove that the commutator of the parabolic Marcinkiewicz integral gΩ with variable kernel is a compact operator on Lp(Rn)  (1<p<∞) if and only if b∈CMO (Rn,ρ). The result is substantial improvement and extension of some known results

On the Compactness of the Commutator of the Parabolic Marcinkiewicz Integral with Variable Kernel