Abstract
We study decay rates for bounded C0-semigroups from the perspective of Lp-infinite-time admissibility and related resolvent estimates. In the Hilbert space setting, polynomial decay of semigroup orbits is characterized by the resolvent behavior in the open right half-plane. A similar characterization based on Lp-infinite-time admissibility is provided for multiplication semigroups on Lq-spaces with 1≤q≤p<∞. For polynomially stable C0-semigroups on Hilbert spaces, we also give a sufficient condition for L2-infinite-time admissibility.
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