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| ON A HYPER HILBERT TRANSFORM |
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Citation： |
CHEN Jiecheng,DING Yong,FAN Dashan.ON A HYPER HILBERT TRANSFORM[J].Chinese Annals of Mathematics B,2003,24(4):475~484 |
| Page view： 1248
Net amount： 1226 |
Authors： |
CHEN Jiecheng; DING Yong;FAN Dashan |
Foundation： |
Project supported by the 973 Project of China (No.G1999075105), the National Natural Science
Foundation of China (No.19631080, No.10271016) and the Zhejiang Provincial Natural Science
Foundation of China (No.RC97017, No.197042). |
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| Abstract： |
The authors define the directional hyper Hilbert transform and
give its 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 $L^p$-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, Fractional integral |
Classification： |
42B25, 42B99 |
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