研究期間：10108~10207;In this proposal a class of singular integral operators associated with a multiparameter family of dilations are studied. We are especially interested in Zygmund dilation on 3 defined by (x, y, z)(1x, 2 y,1 2z) , 1 2 , 0. We introduce a class of singular integral operators associated with this dilation. The kernels of these operators are characterized by a certain regularity and several cancellation conditions. The Lp and H p boundedness of such operators will be proved, and the composition of these operators is considered as well. Examples and applications are also discussed.