... and gave anothercharacterization of BMO space. The purpose of this paper is to give a characterization of BMO space by the boundedness of the commutators of μΩ, μS,andμ∗,λon the generalized ... and the parameterized Littlewood-Paley operators are neither the convolution operator nor the linear operators, hence, we need new ideas and nontrivialestimates in the proof.2. Proof of Theorem ... <p<∞,thenb ∈ BMORn.Remark 1.5. It is easy to check that b, μSfx ≤ 2λnb, μ∗,λfxsee, e.g., the proof of 19 in 15, page 89, we therefore give only the proofs of Theorem...