| 振荡型积分对极大函数的估计 |
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| 引用本文： | 桂易清.振荡型积分对极大函数的估计[J].南昌大学学报(理科版),2006,30(4):325-326,330. |
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| 作者姓名： | 桂易清 |
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| 作者单位： | 华南师范大学,数学学院,广东,广州,510631 |
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| 摘 要： | 首先将2维KaKeya型的极大函数通过Fourier变换转化成振荡型积分的形式，对此振荡型积分作相应的估计。通过Littlewood—Paley方法将此振荡型积分分解成不同的算子，在估计极大算子时，通过Newton—Leibnig公式，将其转化为相应的积分形式，最后通过经典的振荡型积分的估计，得到最后的结果，本方法强调振荡型积分的方法和以前几何测度论的方法不同。
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| 关 键 词： | 傅立叶变换 振荡型积分 KaKeya型极大函数 |
| 文章编号： | 1006-0464（2006）04-0325-02 |
| 收稿时间： | 2006-05-09 |
| 修稿时间： | 2006-05-09 |
The Application of Oscillatory Integrals in Maximal Function Estimate |
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| GUI Yi-qing.The Application of Oscillatory Integrals in Maximal Function Estimate[J].Journal of Nanchang University(Natural Science),2006,30(4):325-326,330. |
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| Authors: | GUI Yi-qing |
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| Institution: | Department of Mathematics, South China Normal University GuangZhou 510631, China |
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| Abstract: | Firstly from Fourier transformation transform the two dimensional maximal of Kakeya type to the oscillatory integrals,then through these oscillatory integrals to get estimate, this paper uses the methods of Littlewood-Paley to divide these oscillatory integrals into different operator. When estimate the maximal operator, from the Newton-Leibnig formula to transform the integral form,last form the classical estimate of oscillatory integral,it get the result. This method emphasises the method of oscillatory integral, different from the geometric measure method as before. |
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| Keywords: | fourior transformation oscillatory integral maximal function |
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