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| BOUNDEDNESS OF MAXIMAL SINGULAR INTEGRALS |
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Citation： |
CHEN Jiecheng,ZHU Xiangrong.BOUNDEDNESS OF MAXIMAL SINGULAR INTEGRALS[J].Chinese Annals of Mathematics B,2005,26(4):559~568 |
| Page view： 1121
Net amount： 718 |
Authors： |
CHEN Jiecheng; ZHU Xiangrong |
Foundation： |
Project supported by the 973 Project of the Ministry of Science and Technology of China (No.G1999075105), the National Natural Science Foundation of China (No.10271107), the Research Fund for the Doctoral Program of Higher Education (No.20030335019) and the Zhejiang Provincial Natural Science Foundation of China (No.RC97017). |
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| Abstract： |
The authors study the singular integrals under the H\"{o}rmander condition and the measure not satisfying the doubling condition. At first, if the corresponding singular integral is bounded from $L^{2}$ to itself, it is proved that the maximal singular integral is bounded from $L^{\infty}$ to $RBMO$ except that it is infinite $\mu$-a.e. on $R^{d}$. A sufficient condition and a necessary condition such that the maximal singular integral is bounded from $L^{2}$ to itself are also obtained. There is a small gap between the two conditions. |
Keywords： |
Maximal singular integral, RBMO |
Classification： |
42B20, 42B25 |
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