Abstract： ForK∈ H1 (Sn- 1 ) and suitable g∈ L1 (R1 + ,rn- 1 dr), the Lp (| x| Tdx ) boundedness of gJ was obtained, where J(x ) = K(x′ )g(| x| ). As a corollary, the Lp (| x| Tdx ) boundedness of the Marcinkiewicz integral operator_K(f ) was obtained. The L2 (| x| Tdx ) boundedness of_K( f ) forKbeing introduced in the paper[6] w as also given.
