The Weiss conjecture and weak norms
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | HAAK, Bernhard Hermann | |
dc.date.accessioned | 2024-04-04T02:24:57Z | |
dc.date.available | 2024-04-04T02:24:57Z | |
dc.date.created | 2012-05-22 | |
dc.date.issued | 2012-12-01 | |
dc.identifier.issn | 1424-3199 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189849 | |
dc.description.abstractEn | In 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.iso | en | |
dc.publisher | Springer Verlag | |
dc.rights.uri | http://hal.archives-ouvertes.fr/licences/copyright/ | |
dc.subject.en | Lorentz spaces | |
dc.subject.en | Weiss conjecture | |
dc.subject.en | Observation of linear systems | |
dc.title.en | The Weiss conjecture and weak norms | |
dc.type | Article de revue | |
dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
dc.subject.hal | Mathématiques [math]/Optimisation et contrôle [math.OC] | |
bordeaux.journal | Journal of Evolution Equations | |
bordeaux.page | 855-861 | |
bordeaux.volume | 12 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.issue | 4 | |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
bordeaux.peerReviewed | oui | |
hal.identifier | hal-00700159 | |
hal.version | 1 | |
hal.popular | non | |
hal.audience | Internationale | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-00700159v1 | |
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