n上傳統單參數的伸縮是定義為(x1,...., xn )( x1,...., xn )， 0.在本計畫中，我們探討一類與多參數伸縮相關的奇異積分算子族。在這些多參數伸縮中，我們最感興趣的就是定義在3 上的Zygmund 伸縮，它是被定義成： 1 2 1 2 (x, y, z)( x, y, z)， 1 2 , 0. 我們想藉由光滑性與消失矩條件來刻畫這類奇異積分算子的核。然後，再處理這些奇異積分算子在Lp與H p空間上的有界性，以及他們的合成算子。此外，我們也會找出一些相關的例子與應用。 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. 研究期間：10008 ~ 10107
