The Weiss conjecture and weak norms
Idioma
en
Article de revue
Este ítem está publicado en
Journal of Evolution Equations. 2012-12-01, vol. 12, n° 4, p. 855-861
Springer Verlag
Resumen en inglés
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 ...Leer más >
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 $L^{p,q}$.< Leer menos
Palabras clave en inglés
Lorentz spaces
Weiss conjecture
Observation of linear systems
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