论文标题
Schrödinger运营商的光谱乘数
Spectral multipliers for Schrödinger operators
论文作者
论文摘要
我们证明了Schrödinger运营商的尖锐Hörmander乘数定理$ h =-Δ+v $ on $ \ mathbb {r}^n $。结果是在特定条件下以加权$ l^\ infty $估计获得的，再加上$ h $的加权$ l^2 $估计，这是一种比通过热核方法获得的非负操作员的条件。我们的方法在一个维度上详细阐述，潜在的$ v $属于某些关键的加权$ l^1 $类。也就是说，我们假设$ \ int（1+ | x |）| v（x）| dx $是有限的，$ h $在零时没有共鸣。在共振情况下，我们假设$ \ int（1+ | x |^2）| v（x）| DX $是有限的。
We prove a sharp Hörmander multiplier theorem for Schrödinger operators $H=-Δ+V$ on $\mathbb{R}^n$. The result is obtained under certain condition on a weighted $L^\infty$ estimate, coupled with a weighted $L^2$ estimate for $H$, which is a weaker condition than that for nonnegative operators via the heat kernel approach. Our approach is elaborated in one dimension with potential $V$ belonging to certain critical weighted $L^1$ class. Namely, we assume that $\int (1+|x|) |V(x)|dx$ is finite and $H$ has no resonance at zero. In the resonance case we assume $\int (1+|x|^2) |V(x)| dx$ is finite.
