ROUGH MULTIPLE SINGULAR INTEGRALS ALONG HYPERSURFACES  

作　　者：邓浏睿 李中凯 马柏林 伍火熊 

机构地区：[1]College of Mathematics and Econometrics, Hunan University [2]School of Mathematical Sciences, Capital Normal University [3]College of Science and Information Engineering, Jiaxing University [4]School of Mathematical Sciences, Xiamen University

出　　处：《Acta Mathematica Scientia》2011年第5期2081-2098,共18页数学物理学报（B辑英文版）

基　　金：Supported by the NSFC (10771054, 10971141, 11071200);the NFS of Beijing (1092004);the NFS of Fujian Province (2010J01013)

摘　　要：In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L（log＋L）ε（Sm-1 × Sn-1） （ε = 1 or 2） supported by hyper-surfaces. The Lp bounds for such singular integral operators as well as the related Marcinkiewicz integral operators are established, provided that the lower dimensional maximal function is bounded on Lq（R3） for all q 1. The condition on the integral kernels is known to be optimal.In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L（log＋L）ε（Sm-1 × Sn-1） （ε = 1 or 2） supported by hyper-surfaces. The Lp bounds for such singular integral operators as well as the related Marcinkiewicz integral operators are established, provided that the lower dimensional maximal function is bounded on Lq（R3） for all q 1. The condition on the integral kernels is known to be optimal.

关 键 词：multiple singular integral Marcinkiewicz integral maximal function HYPERSURFACE rough kernelε 

分 类 号：O186.11[理学—数学]