L2(Rn) boundedness for commutators of oscillatory singular integral operators |
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| Authors: | Ma Bolin and Hu Guoen |
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| Institution: | (1) Department of Applied Mathematics, University of Information Engineering, P.O. Box 1001-747, Zhengzhou 450002, P. R. China;(2) Institute of Applied Mathematics, Hunan University, Changsha 410082, P. R. China;(3) Lab. Mathematics and Its Application, Peking University, Beijing 100871, P. R. China |
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| Abstract: | The commutators of oscillatory singular integral operators with homogeneous kernel \fracW(x)| x |n \frac{{\Omega (x)}}{{\left| x \right|^n }} are studied, where Ω is homogeneous of degree zero, has mean value zero on the unit sphere. It is proved that Ω∈L (logL)K+1(Sn-1) is a sufficient condition under which the k-th order commutator is bounded on L2(Rn). |
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