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This paper is devoted in characterizing the central BMO space via the commutator of the fractional Hardy operator with rough kernel. Precisely, by a more explicit decomposition of the operator and the kernel function, we will show that if the symbol function belongs to the central BMO space, then the commutator are bounded on Lebesgue space. Conversely, the boundedness of the commutator implies that the symbol function belongs to the central BMO space by exploiting the center symmetry of the Hardy operator deeply.

A Characterization of Central BMO Space via the Commutator of Fractional Hardy Operator