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Cases of equality and strict inequality in the extended Hardy–Littlewood inequalities*
Published online by Cambridge University Press: 12 July 2007
Abstract
Extended Hardy-Littlewood inequalities are
where {ui}1≤i≤m are non-negative functions and
denote their Schwarz symmetrization.
In this paper, we determine appropriate conditions under which equality in (*) occurs if and only if {ui}1≤i≤m are Schwarz symmetric.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 3 , June 2005 , pp. 643 - 662
- Copyright
- Copyright © Royal Society of Edinburgh 2005
References
* Dedicated to the senior of symmetrization inequalities, E. H. Lieb, on the occasion of his 70th birthday.
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