| This dissertation is devoted to the boundedness of multilinear Calderon-Zygmund singular integral operators, and obtains some weighted norm inequalities for the m-linear operator with Calderon-Zygmund kernel. It is also given some weighted norm inequalities with general weights for the maximal multilinear Calderon-Zygmund operators. At last, we establish some inequalities on weaker smoothness condition. The main results are as follows:Chapter 2 is concerned with some weighted norm inequalities for the m-linear operator with Calderon-Zygmund kernel in analogy with the weighted estimate for the classical Calderon-Zyg-mund operators which are established by Perez and Cruz-Uribe. First of all, this charpter proposes a weighted weak type endpoint estimate for the multilinear Calderon-Zygmund operators. Then it establishes weighted norm inequalities for the m-linear operator with Calderon-Zygmund kernel with the weighted estimates of classical singular integral operators introduced by Stein and Weiss and multilinear interpolation theorem introduced by Grafakos and Kalton. At last, we establish the new weightes norm inequalities with two-weight norm inequalities of classical singular integral operators.Chapter 3 deals with some weighted norm inequalities with general weights for the maximal multilinear Calderon-Zygmund operators, in analogy with the weighted estimate for the classical maximal Calderon-Zygmund operators which are proved by Hu, Shi and Zhang. The results express the weighted estimates with maximal multilinear Calderon-Zygmund singular integral operators are far more complex than the weighted estimate for the classical Calderon-Zygmund operators.The purpose of chapter 4 is to establish the boundedness of multilinear singular integral operators on spaces of LP1:(Rn)×…×LPm(Rn(1≤p1…,pm<∞) whose kernel satisfies the standard size condition and weaker smoothness condition, and we apply the method of the Calderon-Zygmund decomposition and multilinear interpolation theorem to solve it.
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