Boundedness of Marcinkiewicz integral with rough kernel on Triebel-Lizorkin spaces

详细信息    查看全文

• 作者：Chun-jie Zhang ; Fang-fang Ren ; Yu-huai Zhang…
• 关键词：Marcinkiewicz integral ; Triebel ; Lizorkin spaces ; A ; O174.5
• 刊名：Journal of Zhejiang University - Science C
• 出版年：2015
• 出版时间：August 2015
• 年：2015
• 卷：16
• 期：8
• 页码：654-657
• 全文大小：229 KB
• 参考文献：Al-Qassem, H.M., Cheng, L.C., Pan, Y., 2012. Boundedness of rough integral operators on Triebel-Lizorkin spaces. Publ. Mat., 56(2):261鈥?77. [doi:10.5565/PUBLMAT_ 56212_01]MathSciNet View Article
  Chen, D.N., Chen, J.C., Fan, D.S., 2005. Rough singular integral operators on Hardy-Sobolev spaces. Appl. Math. J. Chin. Univ., 20(1):1鈥?. [doi:10.1007/s11766- 005-0030-8]MathSciNet View Article
  Chen, J.C., Zhang, C.J., 2008. Boundedness of rough singular integral operators on the Triebel-Lizorkin spaces. J. Math. Anal. Appl., 337(2):1048鈥?052. [doi:10.1016/ j.jmaa.2007.04.026]MathSciNet View Article
  Chen, J.C., Fan, D.S., Ying, Y.M., 2002. Singular integral operators on function spaces. J. Math. Anal. Appl., 276(2):691鈥?08. [doi:10.1016/S0022-247X(02)00419-5]MathSciNet View Article
  Chen, J.C., Fan, D.S., Ying, Y.M., 2003. Certain operators with rough singular kernels. Can. J. Math., 55(3): 504鈥?32.MathSciNet View Article
  Chen, J.C., Jia, H.Y., Jiang, L.Y., 2005. Boundedness of rough oscillatory singular integral on Triebel-Lizorkin spaces. J. Math. Anal. Appl., 306(2):385鈥?97. [doi:10. 1016/j.jmaa.2005.01.015]MathSciNet View Article
  Chen, Q.L., Zhang, Z.F., 2004. Boundedness of a class of super singular integral operators and the associated commutators. Sci. China Ser. A, 47(6):842鈥?53. [doi:10.1360/03ys0099]MathSciNet View Article
  Chen, Y.P., Ding, Y., 2008. Rough singular integrals on Triebel-Lizorkin space and Besov space. J. Math. Anal. Appl., 347(2):493鈥?01. [doi:10.1016/j.jmaa.2008.06.039]MathSciNet View Article
  Chen, Y.P., Zhu, K., 2014. Lp bounds for the commutators of oscillatory singular integrals with rough kernels. Abs. Appl. Anal., 2014: 393147.1-393147.8. [doi:10.1155/2014/393147]
  Zhang, C.J., Chen, J.C., 2009. Boundedness of g-functions on Triebel-Lizorkin spaces. Taiwan. J. Math., 13(3): 973鈥?81.MathSciNet
  Zhang, C.J., Chen, J.C., 2010a. Boundedness of singular integrals and maximal singular integrals on Triebel-Lizorkin spaces. Int. J. Math., 21(2):157鈥?68. [doi:10.1142/S0129167X10005982]View Article
  Zhang, C.J., Chen, J.C., 2010b. Boundedness of Marcinkiewicz integral on Triebel-Lizorkin spaces. Appl. Math. J. Chin. Univ., 25(1):48鈥?4. [doi:10.1007/s11766-010-2086-3]View Article
  Zhang, C.J., Zhang, Y.D., 2013. Boundedness of oscillatory singular integral with rough kernels on Triebel-Lizorkin spaces. Appl. Math. J. Chin. Univ., 28(1):90鈥?00. [doi:10.1007/s11766-013-3033-x]View Article
  
• 作者单位：Chun-jie Zhang (1)
  Fang-fang Ren (1)
  Yu-huai Zhang (1)
  Gui-lian Gao (1)
  
  1. Department of Mathematics, Hangzhou Dianzi University, Hangzhou, 310016, China
  
• 刊物类别：Computer Science
• 刊物主题：Computer Science, general
  
• 出版者：Zhejiang University Press, co-published with Springer
• ISSN：1869-196X

文摘

This paper is a continuation of our previous work (Zhang and Chen, 2010b). Following the same general steps of the proof there, we make essential improvement on our previous theorem by recalculating a key inequality. Our result shows that the Marcinkiewicz integral, with a bounded radial function in its kernel, is still bounded on the Triebel-Lizorkin space.