Rozendaal, JanVeraar, Mark2020-04-230022-1236http://hdl.handle.net/1885/203396We study polynomial and exponential stability for C0-semigroups using the recently developed theory of operator-valued (Lp,Lq) Fourier multipliers. We characterize polynomial decay of orbits of a C0-semigroup in terms of the (Lp,Lq) Fourier multiplier properties of its resolvent. Using this characterization we derive new polynomial decay rates which depend on the geometry of the underlying space. We do not assume that the semigroup is uniformly bounded, our results depend only on spectral properties of the generator. As a corollary of our work on polynomial stability we reprove and unify various existing results on exponential stability, and we also obtain a new theorem on exponential stability for positive semigroups.The first author is partially supported by grant DP160100941 of the Australian Research Council. The second author is supported by the VIDI subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO).application/pdfen-AU© 2018 Elsevier Inchttps://creativecommons.org/licenses/by-nc-nd/4.0/C0-semigroup Polynomial and exponential stability Fourier multipliers Type and cotype201810.1016/j.jfa.2018.06.0152019-11-25Creative Commons Attribution Non-Commercial No Derivatives License