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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

Hichem Hajaiej
Hichem Hajaiej
Affiliation:
IACS–FSB, Section de Mathématiques, EPFL, CH-1015 Lausanne, Switzerland (hichem.hajaiej@epfl.ch)
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Abstract

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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