On the 𝐿^{𝑝} boundedness of the wave operators for fourth order Schrödinger operators

Goldberg, Michael; Green, William

doi:10.1090/tran/8377

On the $L^p$ boundedness of the wave operators for fourth order Schrödinger operators
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by Michael Goldberg and William R. Green PDF

Trans. Amer. Math. Soc. 374 (2021), 4075-4092 Request permission

Abstract:

We consider the fourth order Schrödinger operator $H=\Delta ^2+V(x)$ in three dimensions with real-valued potential $V$. Let $H_0=\Delta ^2$, if $V$ decays sufficiently and there are no eigenvalues or resonances in the absolutely continuous spectrum of $H$ then the wave operators $W_{\pm }= s\text { –}\lim _{t\to \pm \infty } e^{itH}e^{-itH_0}$ extend to bounded operators on $L^p(\mathbb R^3)$ for all $1<p<\infty$.

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