The Weiss conjecture and weak norms
Language
en
Article de revue
This item was published in
Journal of Evolution Equations. 2012-12-01, vol. 12, n° 4, p. 855-861
Springer Verlag
English Abstract
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 ...Read more >
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 $L^{p,q}$.Read less <
English Keywords
Lorentz spaces
Weiss conjecture
Observation of linear systems
Origin
Hal imported