On rough singular integrals related to homogeneous mappings

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• 作者：Feng Liu ; Suzhen Mao ; Huoxiong Wu
• 关键词：Singular integrals ; Rough kernels ; Homogeneous mappings ; Extrapolation ; 42B20 ; 42B25
• 刊名：Collectanea Mathematica
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：67
• 期：1
• 页码：113-132
• 全文大小：560 KB
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• 作者单位：Feng Liu (1)
  Suzhen Mao (2)
  Huoxiong Wu (2)
  
  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, Shandong, People’s Republic of China
  2. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, Fujian, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  Analysis
  Applications of Mathematics
  Geometry
  
• 出版者：Springer Milan
• ISSN：2038-4815

文摘

In this paper, we consider the singular integrals related to homogeneous mappings as well as the corresponding maximal truncated singular integrals. Under the rather weak size conditions on the integral kernels both on the unit sphere and in the radial direction, the \(L^p\) bounds for such operators are given, which essentially improve and generalize some known results. Keywords Singular integrals Rough kernels Homogeneous mappings Extrapolation