A note on certain square functions on product spaces  

作　　者：WANG Meng, CHEN Jiecheng2 & FAN Dashan Department of Mathematics, Zhejiang University (at Yuquan campus), Hangzhou 310027, China Department of Mathematics, Zhejiang University (at Xixi campus), Hangzhou 310028, China Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI53201, USA 

出　　处：《Science China Mathematics》2006年第1期98-108,共11页中国科学：数学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.10571156);National Fund of 973 Project(Grant No.G1999075105);Zhejiang Provincial Natural Science Foundation of China(Grant No.RC97017);Research Fund for the Dectoral Program of Higher Education(Grant No.20030335019).

摘　　要：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∈ e Llog+ L(Sn-1 × Sm-1) satisfying the cancellation condition.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.

关 键 词：SQUARE function  MARCINKIEWICZ integral  PRODUCT space. 

分 类 号：O174[理学—数学]