Rearrangement inequalities for functionals with monotone integrands

Simple item page
dc.creatorBurchard, Almut
dc.creatorHajaiej, Hichem
dc.date2005-06-17
dc.date2006-04-06
dc.date.accessioned2026-07-07T06:42:28Z
dc.date.available2026-07-07T06:42:28Z
dc.descriptionThe rearrangement inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands of the form F(u_1,..., u_m) where F is supermodular; in particular, they hold when F has nonnegative mixed second derivatives. This paper concerns the regularity assumptions on F and the equality cases. It is shown here that extended Hardy-Littlewood and Riesz inequalities are valid for supermodular integrands that are just Borel measurable. Under some nondegeneracy conditions, all equality cases are equivalent to radially decreasing functions under transformations that leave the functionals invariant (i.e., measure-preserving maps for the Hardy-Littlewood inequality, translations for the Riesz inequality). The proofs rely on monotone changes of variables in the spirit of Sklar's theorem.
dc.description20 pages. Slightly re-organized, four added references
dc.identifierhttps://arxiv.org/abs/math/0506336
dc.identifierhttp://arxiv.org/abs/math/0506336
dc.identifierJournal of Functional Analysis 233: 561-582 (2006)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/102050
dc.subjectFunctional Analysis
dc.subject26D15
dc.titleRearrangement inequalities for functionals with monotone integrands
dc.typetext

Files

Collections

arXiv