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The Weiss conjecture and weak norms

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorHAAK, Bernhard Hermann
dc.date.accessioned2024-04-04T02:24:57Z
dc.date.available2024-04-04T02:24:57Z
dc.date.created2012-05-22
dc.date.issued2012-12-01
dc.identifier.issn1424-3199
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189849
dc.description.abstractEnIn this note we show that for analytic semigroups the so-called Weiss condition of uniform boundedness of the operators \[ Re(\lambda)^\einhalb C(\lambda+A)^{-1}, \qquad Re(\lambda)>0 \] on the complex right half plane and weak Lebesgue $L^{2,\infty}$--admissibility are equivalent. Moreover, we show that the weak Lebesgue norm is best possible in the sense that it is the endpoint for the 'Weiss conjecture' within the scale of Lorentz spaces $L^{p,q}$.
dc.language.isoen
dc.publisherSpringer Verlag
dc.rights.urihttp://hal.archives-ouvertes.fr/licences/copyright/
dc.subject.enLorentz spaces
dc.subject.enWeiss conjecture
dc.subject.enObservation of linear systems
dc.title.enThe Weiss conjecture and weak norms
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
bordeaux.journalJournal of Evolution Equations
bordeaux.page855-861
bordeaux.volume12
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00700159
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00700159v1
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