The L-continuity of wave operators for higher order Schrödinger operators

نویسندگان

چکیده

We consider the higher order Schr\"odinger operator $H=(-\Delta)^m+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2m$, $m\in \mathbb N$, $m>1$. When is odd, we prove that wave operators extend to bounded on $L^p(\mathbb R^n)$ for all $1\leq p\leq\infty$ under and $m$ dependent conditions analogous case $m=1$. Further, if small certain norms, depend $m$, are same range even $n$. further show smallness assumption removed remain $1<p<\infty$.

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ژورنال

عنوان ژورنال: Advances in Mathematics

سال: 2022

ISSN: ['1857-8365', '1857-8438']

DOI: https://doi.org/10.1016/j.aim.2022.108450