The Weiss conjecture and weak norms
Langue
en
Article de revue
Ce document a été publié dans
Journal of Evolution Equations. 2012-12-01, vol. 12, n° 4, p. 855-861
Springer Verlag
Résumé en anglais
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 ...Lire la suite >
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 $L^{p,q}$.< Réduire
Mots clés en anglais
Lorentz spaces
Weiss conjecture
Observation of linear systems
Origine
Importé de halUnités de recherche