Volume 4,  Issue 3 (GI8), 2003

Article 61



SE- 971 87 LULEA 
E-Mail: annaw@sm.luth.se

Received 12 December, 2002; Accepted 08 September, 2003.
Communicated by: B. Opic

ABSTRACT.    A new necessary and sufficient condition for the weighted Hardy inequality is proved for the case $ 1<p\leq q<\infty $. The corresponding limiting Pólya-Knopp inequality is also proved for $ 0<p\leq q<\infty $. Moreover, a corresponding limiting result in two dimensions is proved. This result may be regarded as an endpoint inequality of Sawyer's two-dimensional Hardy inequality. But here we need only one condition to characterize the inequality whereas in Sawyer's case three conditions are necessary.
Key words:
Inequalities, Weights, Hardy's inequality, Pólya-Knopp's inequality, Multidimensional inequalities, Sawyer's two-dimensional operator.

2000 Mathematics Subject Classification:

Download this article (PDF):

Suitable for a printer:    

Suitable for a monitor:        

To view these files we recommend you save them to your file system and then view by using the Adobe Acrobat Reader. 

That is, click on the icon using the 2nd mouse button and select "Save Target As..." (Microsoft Internet Explorer) or "Save Link As..." (Netscape Navigator).

See our PDF pages for more information.


Other papers in this issue

Report of the General Inequalities 8 Conference; September 15-21, 2002, Noszvaj, Hungary
Compiled by Zsolt Páles

Convolution Inequalities and Applications
Saburou Saitoh, Vu Kim Tuan and Masahiro Yamamoto

The Hardy-Landau-Littlewood Inequalities with Less Smoothness
Constantin P. Niculescu and Constantin Buse

Continuity Properties of Convex-type Set-Valued Maps
Kazimierz Nikodem

Carleman's Inequality - History, Proofs and Some New Generalizations
Maria Johansson, Lars-Erik Persson and Anna Wedestig

Andersson's Inequality and Best Possible Inequalities
A.M. Fink  

On Some Results Involving the Cebysev Functional and its Generalisations
P. Cerone

Separation and Disconjugacy
R.C. Brown

New Norm Type Inequalities for Linear Mappings
Saburou Saitoh

An Integral Approximation in Three Variables
A. Sofo

On Some Spectral Results Relating to the Relative Values of Means
C.E.M. Pearce

On Zeros of Reciprocal Polynomials of Odd Degree
Piroska Lakatos and László Losonczi

Some New Hardy Type Inequalities and their Limiting Inequalities
Anna Wedestig

Generalizations of the Triangle Inequality
Saburou Saitoh

A Survey on Cauchy-Bunyakovsky-Schwarz Type Discrete Inequalities
S.S. Dragomir


Other issues


© 2000 School of Communications and Informatics, Victoria University of Technology. All rights reserved.
JIPAM is published by the School of Communications and Informatics which is part of the Faculty of Engineering and Science, located in Melbourne, Australia. All correspondence should be directed to the editorial office.