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arXiv · 2303.13985

The $L^p$-boundedness of wave operators for fourth order Schr\"odinger operators on ${\mathbb R}^4$

Artbazar Galtbayar·Kenji Yajima
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Abstract

We prove that the wave operators of scattering theory for the fourth order Schr\"odinger operators $\Delta^2 + V(x)$ in ${\mathbb R}^4$ are bounded in $L^p({\mathbb R}^4)$ for the set of $p$'s of $(1,\infty)$ depending on the kind of spectral singularities of $H$ at zero which can be described by the space of bounded solutions of $(\Delta^2 + V(x))u(x)=0$.

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Artbazar Galtbayar, Kenji Yajima. 2023-03-24. The $L^p$-boundedness of wave operators for fourth order Schr\"odinger operators on ${\mathbb R}^4$. https://arxiv.org/abs/2303.13985

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