The Hardy Spaces Estimates for the Commutator of Marcinkiewicz Integral
Received:December 18, 2006  Revised:September 04, 2007
Key Word: commutator   Marcinkiewicz integral   Lipschitz space   Hardy space   Herz type Hardy space.
Fund ProjectL:the National Natural Science Foundation of China (No.10371080); the Key Program Foundation of Ministry of Education of China (No.108136).
 Author Name Affiliation WANG Hong Bin Department of Mathematics, China University of Mining and Technology (Beijing), Beijing 100083, China LIU Zong Guang Department of Mathematics, China University of Mining and Technology (Beijing), Beijing 100083, China
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In this paper, we obtain the $(H^1,L^{n/(n-\beta)})$ and $(H\dot{K}^{n(1-1/q_1),p}_{q_1},\dot{K}^{n(1-1/q_1),p}_{q_2})$ type estimates for the commutator of Marcinkiewicz integral with the kernel satisfying the logarithmic type Lipschitz conditions.