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Rough multiple singular integrals along hypersurfaces |
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| Authors: | Deng Liurui Li Zhongkai Ma Bolin Wu Huoxiong |
| Affiliation: | aCollege of Mathematics and Econometrics, Hunan University, Changsha 410082, China;bSchool of Mathematical Sciences, Capital Normal University, Beijing 100048, China;cCollege of Science and Information Engineering, Jiaxing University, Jiaxing 314001, China;dSchool of Mathematical Sciences, Xiamen University, Xiamen 361005, China |
| Abstract: | 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. |
| Keywords: | multiple singular integral Marcinkiewicz integral maximal function hyper-surface rough kernel |
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