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| ON A HYPER HILBERT TRANSFORM＊＊＊＊ | |
| 作者姓名： | CHEN Jiecheng DING Yong FAN Dashan |
| 作者单位： | CHEN JIECHENG DING YONG FAN DASHAN Department of Mathematics，Zhejiang University，Hangzhou 310028，China. Department of Mathematics，Beijing Normai University，Beijing 100875，China. Department of Mathematics，University of Wisconsin，Milwaukee，WI 53201，USA. |
| 基金项目： | the 973 Project of China(No.G1999075105)，the National Natural ScienceFoundation of China(No.19631080,No.10271016)，the Zhejiang Provincial Natural ScienceFoundation of China(No.RC97017,No.197042). |
| 摘 要： | The authors define the directional hyper Hilbert transform and give ita mixed norm estimate. The similar conclusions for the directional fractional integral of one dimension are also obtained in this paper. As an application of the above results, the authors give the Lp-boundedness for a class of the hyper singular integrals and the fractional integrals with variable kernel. Moreover, as another application of the above results, the authors prove the dimension free estimate for the hyper Riesz transform. This is an extension of the related result obtained by Stein. |
| 关 键 词： | 超Hilbert变换 Sobolev空间 奇异积分 分数次积分 维数自由估计 混合范数估计 |
| 收稿时间： | 6/2/2017 12:00:00 AM |
ON A HYPER HILBERT TRANSFORM |
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| CHEN Jiecheng,DING Yong,FAN Dashan.ON A HYPER HILBERT TRANSFORM[J].Chinese Annals of Mathematics,Series B,2003,24(4):475-484. | |
| Authors: | CHEN Jiecheng DING Yong and FAN Dashan |
| Institution: | 1. Department of Mathematics, Zhejiang University, Hangzhou 310028, China 2. Department of Mathematics, Beijing Normal University, Beijing 100875, China 3. Department of Mathematics, University of Wisconsin, Milwaukee, WI 53201, USA |
| Abstract: | The authors define the directional hyper Hilbert transform and give ita mixed norm estimate. The similar conclusions for the directional fractional integral of one dimension are also obtained in this paper. As an application of the above results, the authors give the Lp-boundedness for a class of the hyper singular integrals and the fractional integrals with variable kernel. Moreover, as another application of the above results, the authors prove the dimension free estimate for the hyper Riesz transform. This is an extension of the related result obtained by Stein. |
| Keywords: | Hyper Hilbert transform Sobolev spaces Dimension free estimate Singular integral Practional integral |
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