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In this paper,the L^2-boundedness of a class of parametric Marcinkiewicz integral μa,h^p with kernel function Ω in Bq^0.0(s^n-1) for some q>1,and the radial function h(x)∈l∞(L^s)(R+) for 1<s≤∞ are given.The L^p(R^n)(2≤p<∞）boundedness of μΩ,k,λ^u,