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| HAL: hal-00700159, version 1 |
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| Available versions: | v1 (2012-05-22) | v2 (2012-06-25) |
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| The Weiss conjecture and weak norms |
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| Bernhard Hermann Haak 1 |
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| (2012-05-22) |
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| 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 $L^{p,q}$. |
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| 1: | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| Subject | : | Mathematics/Functional Analysis Mathematics/Optimization and Control |
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| Observation of linear systems – Weiss conjecture – Lorentz spaces |
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| hal-00700159, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00700159 | |
| oai:hal.archives-ouvertes.fr:hal-00700159 | |
| From: Bernhard Hermann Haak | |
| Submitted on: Tuesday, 22 May 2012 14:34:58 | |
| Updated on: Tuesday, 22 May 2012 14:48:28 | |
