| 非双倍条件下极大奇异积分算子的估计 |
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| 作者姓名： | Ruan Jianmiao Zhu Xiangrong |
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| 作者单位： | [1]Dept. of Math. , Zhejiang Univ. , Hangzhou 310028,China. [2]Dept. of Math. , Zhejiang Education Institute,Hangzhou 310012,China. |
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| 基金项目： | Supported by the Science Foundation of the Education Department of Zhejiang Province （20050316）. |
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| 摘 要： | It is shown that the maximal singular integral operator with kernels satisfying Ho rmander＇s condition is of weak type （1,1） and L^p （1〈p〈∞） bounded without assuming that the underlying measure p is doubling. Under stronger smoothness conditions,such estimates can be obtained by using a Cotlar＇s inequality. This inequality is not applicable here and it is noticeable that the Cotlar＇s inequality maybe fails under Hormander＇s condition.
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| 关 键 词： | Calderon-Zygmund理论 最大单积分 双倍测度 强光滑 Cotlar不等式 |
| 收稿时间： | 2004-02-18 |
Estimates for the maximal singular integrals without doubling condition |
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| Ruan Jianmiao Zhu Xiangrong.Estimates for the maximal singular integrals without doubling condition[J].Applied Mathematics A Journal of Chinese Universities,2005,20(4):448-454. |
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| Authors: | Ruan Jianmiao Zhu Xiangrong |
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| Institution: | Dept.of Math., Zhejiang Univ., Hangzhou 310028,China;Dept.of Math., Zhejiang Univ., Hangzhou 310028,China;Dept.of Math., Zhejiang Education Institute,Hangzhou 310012,China |
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| Abstract: | It is shown that the maximal singular integral operator with kernels satisfying Hő rmander's condition is of weak type (1,1)
and L
p (1<p<∞) bounded without assuming that the underlying measure μ is doubling. Under stronger smoothness conditions, such estimates
can be obtained by using a Cotlar's inequality. This inequality is not applicable here and it is noticeable that the Cotlar's
inequality maybe fails under Hormander's condition.
Supported by the Science Foundation of the Education Department of Zhejiang Province (20050316). |
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| Keywords: | Calderon-Zygmund theory maximal singular integral nondoubling measure |
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