### Weighted Inequalities of Hardy-Type on Amalgams

Pankaj Jain and Suket Kumar
Source: Real Anal. Exchange Volume 34, Number 2 (2008), 483-500.

#### Abstract

Weighted Hardy-type inequalities between suitable amalgams $\ell^q(L^{p},u)$ and $\ell^{\bar q}(L^{\bar p},v)$ are characterized. The Hardy-type operator involved in the inequalities involves functions which are not necessarily non-negative.

First Page:
Primary Subjects: 26D10, 26D15
Secondary Subjects: 26A05
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

Permanent link to this document: http://projecteuclid.org/euclid.rae/1256835200
Zentralblatt MATH identifier: 05652549
Mathematical Reviews number (MathSciNet): MR2569200

### References

C. Carton-Lebrun, H. P. Heinig, S. C. Hofmann, Integral operators on weighted amalgams, Studia Math. 109(2) (1994), 133–157.
Mathematical Reviews (MathSciNet): MR1269772
Zentralblatt MATH: 0824.42015
A. Kufner, L. Maligranda and L.-E. Persson, The Hardy Inequality: About its History and Some Related Results, Vydavatelsky Sevis Pub. House, Pilsen, 2007.
Mathematical Reviews (MathSciNet): MR2351524
A. Kufner and L.-E. Persson, Weighted Inequality of Hardy Type, World Scientific, New Jersey/London/Singapore/Hong Kong, 2003.
Mathematical Reviews (MathSciNet): MR1982932
Zentralblatt MATH: 1065.26018
V. D. Stepanov, Weighted norm inequalities for integral operators and related topics, in Proceedings of the Spring School “Nonlinear Analysis, Function Spaces and Applications”, 1994, 139–175.
Mathematical Reviews (MathSciNet): MR1322312
Zentralblatt MATH: 0866.47025
P. A. Zharov, On a two-weight inequality, Generalization of inequalities of Hardy and Poincáre (Russian), Trudy Math. Ins. Steklov, 194 (1992), 97–110; translation in Proc. Steklov Inst. Math., 194(4) (1993), 101–114.
Mathematical Reviews (MathSciNet): MR1289650