The authors study the singular integrals under the Hormander 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 prove...The authors study the singular integrals under the Hormander 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^∞ to RBMO except that it is infinite μ-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.展开更多
基金Project supported by the 973 Project of the Ministry of Science and Technology of China (No.G1999 075105) the National Natural Science Foundation of China (No. 10271107) the Research Fund for the Doctoral Program of Higher Education (No.20030335019) the Zhejiang Provincial Natural Science Foundation of China (No.RC97017).
文摘The authors study the singular integrals under the Hormander 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^∞ to RBMO except that it is infinite μ-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.
