薛定谔群的精确$L^p$估计
Sharp $L^p$ estimates for Schrödinger groups
摘要：
考虑$L^2(\mathbb{R}^d)$中的非负自伴算子$H$。我们假设它的热算子$e^{-tH}$对某些指数$p_0\in[0,2)$满足非对角代数衰减估计。然后，我们证明了尖锐的$L^p\to L^p$频率截断估计薛定谔集团$e^{itH}$ $p\in[p_0,p'_0]$。特别是，我们的结果适用于每一个运营商的形式$H=(i\nabla+A)^2+V$，磁势$A\in L^2_{loc}(\mathbb{R}^d,\mathbb{R}^d)$和电位$V$的积极和消极的部分是在当地的加藤类和加藤类，分别。
英文摘要：
Consider a non-negative self-adjoint operator $H$ in $L^2(\mathbb{R}^d)$. We suppose that its heat operator $e^{-tH}$ satisfies an off-diagonal algebraic decay estimate, for some exponents $p_0\in[0,2)$. Then we prove sharp $L^p\to L^p$ frequency truncated estimates for the Schrödinger group $e^{itH}$ for $p\in[p_0,p'_0]$. In particular, our results apply to every operator of the form $H=(i\nabla+A)^2+V$, with a magnetic potential $A\in L^2_{loc}(\mathbb{R}^d,\mathbb{R}^d)$ and an electric potential $V$ whose positive and negative parts are in the local Kato class and in the Kato class, respectively.
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