Skip to content

Advertisement

  • Research Article
  • Open Access

Weighted weak-type inequalities for generalized Hardy operators

  • 1Email author,
  • 2 and
  • 2
Journal of Inequalities and Applications20062006:62426

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

  • Received: 13 June 2006
  • Accepted: 21 September 2006
  • Published:

Abstract

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

Keywords

  • Monotonicity Condition
  • Hardy Operator
  • Generalize Hardy Operator

[123456]

Authors’ Affiliations

(1)
IMAL-CONICET, Güemes 3450, Santa Fe, 3000, Argentina
(2)
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Málaga, 29071, Spain

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 MathematicsGoogle Scholar
  2. Chen T, Sinnamon G: Generalized Hardy operators and normalizing measures. Journal of Inequalities and Applications 2002,7(6):829–866. 10.1155/S1025583402000437MathSciNetMATHGoogle 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/S1025583499000272MathSciNetMATHGoogle 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/S0024611599012010MathSciNetView ArticleMATHGoogle 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/S0002-9939-98-04247-6MathSciNetView ArticleMATHGoogle Scholar
  6. Prokhorov DV: Weighted estimates for Riemann-Liouville operators with variable limits. Siberian Mathematical Journal 2003,44(6):1049–1060.MathSciNetView ArticleMATHGoogle Scholar

Copyright

© A. L. Bernardis et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advertisement