Skip to main content
  • Research Article
  • Open access
  • Published:

Weighted weak-type inequalities for generalized Hardy operators

Abstract

We characterize the pairs of weights for which the Hardy-Steklov-type operator applies into weak-,, assuming certain monotonicity conditions on,, and.

[123456]

References

  1. Bernardis AL, Martín-Reyes FJ, Ortega Salvador P: Weighted inequalities for Hardy-Steklov operators. to appear in Canadian Journal of Mathematics to appear in Canadian Journal of Mathematics

  2. Chen T, Sinnamon G: Generalized Hardy operators and normalizing measures. Journal of Inequalities and Applications 2002,7(6):829–866. 10.1155/S1025583402000437

    MathSciNet  MATH  Google Scholar 

  3. Gogatishvili A, Lang J: The generalized Hardy operator with kernel and variable integral limits in Banach function spaces. Journal of Inequalities and Applications 1999,4(1):1–16. 10.1155/S1025583499000272

    MathSciNet  MATH  Google Scholar 

  4. Lai Q: Weighted modular inequalities for Hardy type operators. Proceedings of the London Mathematical Society. Third Series 1999,79(3):649–672. 10.1112/S0024611599012010

    Article  MathSciNet  MATH  Google Scholar 

  5. Martín-Reyes FJ, Ortega Salvador P: On weighted weak type inequalities for modified Hardy operators. Proceedings of the American Mathematical Society 1998,126(6):1739–1746. 10.1090/S0002-9939-98-04247-6

    Article  MathSciNet  MATH  Google Scholar 

  6. Prokhorov DV: Weighted estimates for Riemann-Liouville operators with variable limits. Siberian Mathematical Journal 2003,44(6):1049–1060.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. L. Bernardis.

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

Bernardis, A.L., Martín-Reyes, F.J. & Ortega Salvador, P. Weighted weak-type inequalities for generalized Hardy operators. J Inequal Appl 2006, 62426 (2006). https://doi.org/10.1155/JIA/2006/62426

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/JIA/2006/62426

Keywords