Sharp Hardy inequalities of fractional order involving slowly varying functions

We establish necessary and sufficient conditions for the validity of Hardy inequalities of fractional orders involving weights which are products of power-type functions and slowly varying functions. Consequently, for such weights, we solve Open Problems 1 and 2 mentioned in the book of Kufner and P...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2012-02, Vol.386 (2), p.728-737
Main Authors: Gurka, Petr, Opic, Bohumír
Format: Article
Language:English
Subjects:
Hardy inequality of fractional order
Slowly varying functions
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We establish necessary and sufficient conditions for the validity of Hardy inequalities of fractional orders involving weights which are products of power-type functions and slowly varying functions. Consequently, for such weights, we solve Open Problems 1 and 2 mentioned in the book of Kufner and Persson, Weighted Inequalities of Hardy Type (World Scientific Publishing, 2003).
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.08.031