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In this note, the author prove that maximal Bocher-Riesz commutator Bbδ , generated by operator Bδ , and function b ∈ BMO(ω) is a bounded operator from Lp(μ) into Lp (ν), where ω∈ (μν-1 )1 p , μ , ν∈ Ap for 1 < p < ∞. The proof relies heavily on the