论文标题
端点上的注释$ l^p $ - 传播者的古典和高级施罗丁运营商的注释
A note on endpoint $L^p$-continuity of wave operators for classical and higher order Schrödinger operators
论文作者
论文摘要
我们考虑高阶Schrödinger运算符$ h =（ - δ）^m+v（x）$ in $ n $ dimensions in $ n $ dimensions，当$ n> 200万$，$ m \ in \ mathbb n $时，带有实价的潜在$ v $。我们以$ m> 1 $的价格调整了我们的最新结果，以表明波动运算符在$ l^p（\ mathbb r^n）$上，全范围$ 1 \ leq p \ leq p \ leq p \ leq \ leq \ leq \ infty $在偶数和奇数尺寸的情况下，而没有假设电势很小。使用的方法在没有区分和奇数的情况下使用，捕获端点$ p = 1，\ infty $，并以某种方式简化了低能参数，即使在经典的情况下，$ m = 1 $。
We consider the higher order Schrödinger operator $H=(-Δ)^m+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2m$, $m\in \mathbb N$. We adapt our recent results for $m>1$ to show that the wave operators are bounded on $L^p(\mathbb R^n)$ for the full the range $1\leq p\leq \infty$ in both even and odd dimensions without assuming the potential is small. The approach used works without distinguishing even and odd cases, captures the endpoints $p=1,\infty$, and somehow simplifies the low energy argument even in the classical case of $m=1$.
