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Certain rearrangement inequalities of a type considered by Hardy, Riesz, andBrascamp-Lieb-Luttinger are studied. Subsets of the real line that extremizethese inequalities are characterized. Our results apply only to special cases,and complement earlier results by Burchard treating other cases.  This draft incorporates minor corrections and clarifications.

Cases of equality in certain multilinear inequalities of Hardy-Riesz-Brascamp-Lieb-Luttinger type