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- W2950213259 abstract "Let X be a metric space with a doubling measure satisfying $$mu (B)gtrsim r_{B}^n$$ for any ball B with any radius $$r_{B}>0$$ . Let L be a non negative selfadjoint operator on $$L^{2}(X)$$ . We assume that $$e^{-tL}$$ satisfies a Gaussian upper bound and that the flow $$e^{itL}$$ satisfies a typical $$L^{1}-L^{infty }$$ dispersive estimate of the form $$begin{aligned} Vert e^{itL}Vert _{L^{1}rightarrow L^{infty }}lesssim |t|^{-frac{n}{2}}. end{aligned}$$ Then we prove a similar $$L^{1}-L^{infty }$$ dispersive estimate for a general class of flows $$e^{it phi (L)}$$ , with $$phi (r)$$ of power type near 0 and near $$infty $$ . In the case of fractional powers $$phi (L)=L^{nu }$$ , $$nu in (0,1)$$ , we deduce dispersive estimates for $$e^{itL^{nu }}$$ with data in Sobolev, Besov or Hardy spaces $$H^{p}_{L}$$ with $$pin (0,1]$$ , associated to the operator L." @default.
- W2950213259 created "2019-06-27" @default.
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- W2950213259 date "2019-06-15" @default.
- W2950213259 modified "2023-10-17" @default.
- W2950213259 title "On the flows associated to selfadjoint operators on metric measure spaces" @default.
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- W2950213259 doi "https://doi.org/10.1007/s00208-019-01857-w" @default.
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