A note on certain square functions on product spaces

We study certain square functions on product spaces Rn × Rm, whose integral kernels are obtained from kernels which are homogeneous in each factor Rn and Rm and locally in L(log+ L) away from Rn × {0} and {0} × Rm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on Lp(Rn × Rm)(p＞1) for Ω ∈ Llog+ L(Sn-1 × Sm-1) satisfying the cancellation condition.

作 者： WANG Meng CHEN Jiecheng FAN Dashan   作者單位： WANG Meng(Department of Mathematics, Zhejiang University at Yuquan campus, Hangzhou 310027, China)

CHEN Jiecheng(Department of Mathematics, Zhejiang University (at Xixi campus), Hangzhou 310028, China)

FAN Dashan(Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI53201, USA) 

刊 名： 中國科學(xué)A輯（英文版）  SCI 英文刊名： SCIENCE IN CHINA (MATHEMATICS)  年，卷(期)： 2006 49(1)  分類號： O1  關(guān)鍵詞： square function   Marcinkiewicz integral   product space  

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