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- W4210360165 abstract "Abstract Let $mathcal {H}=-Delta + |x|^2$ be the Hermite operator on $mathbb R^n$ with $nge 2$. In this paper, we prove the boundedness of Schrödinger groups of fractional powers of $mathcal {H}$ on Lebesgue and Hardy spaces. More precisely, we prove that (a) for $p in (1,infty )$, $gamma>0$ and $beta /gamma geq n|1/p -1/2|$, $$ begin{align*} big|mathcal{H}^{-beta /2}e^{it mathcal{H}^{gamma /2}}fbig|_{L^p(mathbb R^n)} leq C (1 + |t|)^{n|1/p-1/2|}|f|_{L^p(mathbb R^n)}, quad forall t in mathbb{R}, end{align*}$$and (b) for $p in (0, 1]$, $gamma>0$ and $beta /gamma geq n(1/p -1/2)$, $$ begin{align*} big|mathcal{H}^{-beta /2}e^{it mathcal{H}^{gamma /2}}fbig|_{H^p_{mathcal{H}}(mathbb R^n)} leq C (1 + |t|)^{n(1/p-1/2)}|f|_{H^p_{mathcal{H}}(mathbb R^n)}, quad forall t in mathbb{R}, end{align*}$$where $H^p_{mathcal {H}}(mathbb R^n)$ is the Hardy space associated with the operator $mathcal {H}$. These estimates improve related result of Thangavelu [22] and have some interesting applications." @default.
- W4210360165 created "2022-02-08" @default.
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- W4210360165 date "2022-03-01" @default.
- W4210360165 modified "2023-09-26" @default.
- W4210360165 title "On Schrödinger Groups of Fractional Powers of Hermite Operators" @default.
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- W4210360165 doi "https://doi.org/10.1093/imrn/rnac037" @default.
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