Skip to main content
Journal of Inequalities and Applications
Download PDF
  • Research Article
  • Open access
  • Published:

On the boundedness of maximal operators and singular operators with kernels in

Journal of Inequalities and Applications volume 2006, Article number: 96732 (2006) Cite this article

Abstract

We establish the-boundedness for a class of singular integral operators and a class of related maximal operators when their singular kernels are given by functions in.

[123456789101112131415161718192021]

References

  1. Al-Qassem HM: bounds for a class of rough maximal operators. preprint preprint

  2. Al-Qassem HM, Pan Y: estimates for singular integrals with kernels belonging to certain block spaces. Revista Matemática Iberoamericana 2002,18(3):701–730.

    Article  MathSciNet  MATH  Google Scholar 

  3. Al-Qassem HM, Pan Y: Singular integrals along surfaces of revolution with rough kernels. SUT Journal of Mathematics 2003,39(1):55–70.

    MathSciNet  MATH  Google Scholar 

  4. Al-Salman A, Pan Y: Singular integrals with rough kernels in. Journal of the London Mathematical Society. Second Series 2002,66(1):153–174. 10.1112/S0024610702003241

    Article  MathSciNet  MATH  Google Scholar 

  5. Ash JM, Ash PF, Fefferman CL, Jones RL: Singular integral operators with complex homogeneity. Studia Mathematica 1979,65(1):31–50.

    MathSciNet  MATH  Google Scholar 

  6. Benedek A, Panzone R: The space, with mixed norm. Duke Mathematical Journal 1961,28(3):301–324. 10.1215/S0012-7094-61-02828-9

    Article  MathSciNet  MATH  Google Scholar 

  7. Calderón AP, Zygmund A: On the existence of certain singular integrals. Acta Mathematica 1952,88(1):85–139. 10.1007/BF02392130

    Article  MathSciNet  MATH  Google Scholar 

  8. Calderón AP, Zygmund A: On singular integrals. American Journal of Mathematics 1956, 78: 289–309. 10.2307/2372517

    Article  MathSciNet  MATH  Google Scholar 

  9. Chen L-K: On a singular integral. Studia Mathematica 1986,85(1):61–72, 1987.

    MathSciNet  MATH  Google Scholar 

  10. Chen L-K, Lin H: A maximal operator related to a class of singular integrals. Illinois Journal of Mathematics 1990,34(1):120–126.

    MathSciNet  MATH  Google Scholar 

  11. Coifman RR, Weiss G: Extensions of Hardy spaces and their use in analysis. Bulletin of the American Mathematical Society 1977,83(4):569–645. 10.1090/S0002-9904-1977-14325-5

    Article  MathSciNet  MATH  Google Scholar 

  12. Ding Y, He Q: Weighted boundedness of a rough maximal operator. Acta Mathematica Scientia. English Edition 2000,20(3):417–422.

    MathSciNet  MATH  Google Scholar 

  13. Duoandikoetxea J, Rubio de Francia JL: Maximal and singular integral operators via Fourier transform estimates. Inventiones Mathematicae 1986,84(3):541–561. 10.1007/BF01388746

    Article  MathSciNet  MATH  Google Scholar 

  14. Fan D, Pan Y: A singular integral operator with rough kernel. Proceedings of the American Mathematical Society 1997,125(12):3695–3703. 10.1090/S0002-9939-97-04111-7

    Article  MathSciNet  MATH  Google Scholar 

  15. Fan D, Pan Y: Singular integral operators with rough kernels supported by subvarieties. American Journal of Mathematics 1997,119(4):799–839. 10.1353/ajm.1997.0024

    Article  MathSciNet  MATH  Google Scholar 

  16. Fan D, Pan Y, Yang D: A weighted norm inequality for rough singular integrals. The Tohoku Mathematical Journal 1999,51(2):141–161. 10.2748/tmj/1178224808

    Article  MathSciNet  MATH  Google Scholar 

  17. Fefferman R: A note on singular integrals. Proceedings of the American Mathematical Society 1979,74(2):266–270. 10.1090/S0002-9939-1979-0524298-3

    Article  MathSciNet  MATH  Google Scholar 

  18. Kim W-J, Wainger S, Wright J, Ziesler S: Singular integrals and maximal functions associated to surfaces of revolution. The Bulletin of the London Mathematical Society 1996,28(3):291–296. 10.1112/blms/28.3.291

    Article  MathSciNet  MATH  Google Scholar 

  19. Le HV: Maximal operators and singular integral operators along submanifolds. Journal of Mathematical Analysis and Applications 2004,296(1):44–64. 10.1016/j.jmaa.2004.02.056

    Article  MathSciNet  MATH  Google Scholar 

  20. Namazi J: A singular integral. Proceedings of the American Mathematical Society 1986,96(3):421–424. 10.1090/S0002-9939-1986-0822432-2

    Article  MathSciNet  MATH  Google Scholar 

  21. Stein EM: Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, no. 30. Princeton University Press, New Jersey; 1970:xiv+290.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Yarmouk University, Irbid, Jordan

    H. M. Al-Qassem

Authors
  1. H. M. Al-Qassem
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. M. Al-Qassem.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Al-Qassem, H.M. On the boundedness of maximal operators and singular operators with kernels in. J Inequal Appl 2006, 96732 (2006). https://doi.org/10.1155/JIA/2006/96732

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/JIA/2006/96732

Keywords