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On the Generalized Marcinkiewicz Integral Operators with Rough Kernels

  • Dashan Fan (a1) and Huoxiong Wu (a2)
Abstract

A class of generalized Marcinkiewicz integral operators is introduced, and, under rather weak conditions on the integral kernels, the boundedness of such operators on Lp and Triebel–Lizorkin spaces is established.

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Footnotes
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D. Fan was partially supported by the NNSF of China (Grant No. 10371046). Huoxiong Wu was the corresponding author and partially supported by the NNSF of China (Grant No. 10571122, 10771054).

Footnotes
References
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[1] Al-Qassem, H., Al-Salman, A., Cheng, L. C., and Pan, Y., Marcinkiewicz integrals on product spaces. Studia Math. 167(2005), no. 3, 227234. doi:10.4064/sm167-3-4
[2] Al-Qassem, H., Al-Salman, A., Cheng, L. C., and Pan, Y., Lp bounds for the function of Marcinkiewicz. Math. Res. Lett. 9(2002), no. 5–6, 697700.
[3] Chen, J., Ding, Y., and Fan, D., Certain square functions on product spaces. Math. Nachr. 230(2001), 518. doi:10.1002/1522-2616(200110)230:1h5::AID-MANA5i3.0.CO;2-O
[4] Chen, J., Fan, D., and Ying, Y., The method of rotation and Marcinkiewicz integrals on product domains. Studia Math. 153(2002), no. 1, 4158. doi:10.4064/sm153-1-4
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[19] Wu, H., Lp bounds for Marcinkiewicz integrals associated to surfaces of revolution. J. Math. Anal. Appl. 321(2006), no. 2, 811827. doi:10.1016/j.jmaa.2005.08.087
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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