| 带振荡因子的粗双曲奇异积分算子 |
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| 引用本文： | 陈杰诚,尤英. 带振荡因子的粗双曲奇异积分算子[J]. 高校应用数学学报(英文版), 2006, 21(2): 179-190. DOI: 10.1007/BF02791355 |
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| 作者姓名： | 陈杰诚 尤英 |
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| 作者单位： | 浙江大学;浙江大学 |
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| 摘 要： | The singular integral operator J Ω,α, and the Marcinkiewicz integral operator (~μ)Ω,α are studied. The kernels of the operators behave like |y|-n-α(α＞0) near the origin, and contain an oscillating factor ei|y|-β(β＞0) and a distribution Ω on the unit sphere Sn-1 It is proved that, if Ω is in the Hardy space Hr (Sn-1) with 0＜r= (n-1)/(n-1 )(＞0), and satisfies certain cancellation condition,then J Ω,α and uΩ,α extend the bounded operator from Sobolev space Lpγ to Lebesgue space Lp for some p. The result improves and extends some known results.
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| 关 键 词： | 振荡因子 粗双曲奇异积分算子 Marcinkiewicz积分算子 Sobolev空间 |
| 收稿时间： | 2005-08-31 |
Rough hypersingular integral operators with an oscillating factor |
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| Chen Jiecheng,You Ying. Rough hypersingular integral operators with an oscillating factor[J]. Applied Mathematics A Journal of Chinese Universities, 2006, 21(2): 179-190. DOI: 10.1007/BF02791355 |
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| Authors: | Chen Jiecheng You Ying |
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| Affiliation: | Dept. 0f Math. , Zhejiang Univ. , Hangzhou 310028,China |
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| Abstract: | The singular integral operator J Ω,α , and the Marcinkiewicz integral operator  are studied. The kernels of the operators behave like |y|-n-α(a>0) near the origin, and contain an oscillating factor ei|y|-β (β>0) and a distribution ω on the unit sphere S n−1. It is proved that, if ω is in the Hardy space H r (S n−1) with 0<r=(n−1)/(n−1+γ)(γ>0), and satisfies certain cancellation condition, then T Ω,α and  extend the bounded operator from Sobolev space L γ ρ to Lebesgue space L p for some p. The result improves and extends some known results. |
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| Keywords: | rough hypersingular integral operator Marcinkiewicz integral operator rough kernel Sobolev space |
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