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数学进展 - 2016, Vol. 45(2): 221-232
研究论文
沿有限型的粗糙核奇异积分算子在乘积空间上的外插估计
Estimates for Rough Singular Integrals Along Submanifolds of Finite Type on Product Domains via Extrapolation Its %Mycielski Graph's Incidence Coloring Number

蓝森华1, 2,张代清3
LAN Senhua1, 2, ZHANG Daiqing3

1. 丽水学院数学系, 丽水, 浙江, 323000;
2. 嘉兴学院数理与信息工程学院, 嘉兴, 浙江, 314001;
3. 厦门大学数学科学学院, 厦门, 福建, 361005
1. Department of Mathematics, Lishui University, Lishui, Zhejiang, 323000, P. R. China;
2. College of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang, 314001;
3. School of Mathematical Sciences, Xiamen University,Xiamen, Fujian, 361005, P. R. China

收稿日期: 2014-07-27
出版日期: 2016-03-10
2016, Vol. 45(2): 221-232
DOI: 10.11845/sxjz.2014116b


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摘要 本文致力于研究乘积空间上沿有限型的奇异积分算子, 通过Fourier变换及外插方法的讨论, 证明了带径向球面粗糙核的奇异积分算子的$L^p(\mathbb{R}^n\times\mathbb{R}^m)$有界性.
Abstract:We consider the singular integrals associated with functions of finite type on product domains. By the delicate Fourier transform estimates and the extrapolation arguments, we obtain the $L^p(\mathbb{R}^n\times\mathbb{R}^m)$ boundedness for such operators with rough kernels both in the radial direction and on the spherical surface.
PACS:  O174.2  
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