Published online by Cambridge University Press: 12 July 2007
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.
* Dedicated to the senior of symmetrization inequalities, E. H. Lieb, on the occasion of his 70th birthday.