Open Access

Weighted weak-type inequalities for generalized Hardy operators

  • A. L. Bernardis1Email author,
  • F. J. Martín-Reyes2 and
  • P. Ortega Salvador2
Journal of Inequalities and Applications20062006:62426

DOI: 10.1155/JIA/2006/62426

Received: 13 June 2006

Accepted: 21 September 2006

Published: 16 November 2006

Abstract

We characterize the pairs of weights https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F62426/MediaObjects/13660_2006_Article_1622_IEq1_HTML.gif for which the Hardy-Steklov-type operator https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F62426/MediaObjects/13660_2006_Article_1622_IEq2_HTML.gif applies https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F62426/MediaObjects/13660_2006_Article_1622_IEq3_HTML.gif into weak- https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F62426/MediaObjects/13660_2006_Article_1622_IEq4_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F62426/MediaObjects/13660_2006_Article_1622_IEq5_HTML.gif , assuming certain monotonicity conditions on https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F62426/MediaObjects/13660_2006_Article_1622_IEq6_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F62426/MediaObjects/13660_2006_Article_1622_IEq7_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F62426/MediaObjects/13660_2006_Article_1622_IEq8_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F62426/MediaObjects/13660_2006_Article_1622_IEq9_HTML.gif .

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Authors’ Affiliations

(1)
IMAL-CONICET
(2)
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga

References

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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.