Lp estimates for fractional Schrödinger operators with Kato class potentials
Lp estimates for fractional Schrödinger operators with Kato class potentials
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具有 Kato 类势的分数薛定谔算子的 L 估计
DOI：
10.1016/j.jde.2018.06.004
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发表时间：
2018
影响因子：
2.4
通讯作者：
Duan Zhiwen
中科院分区：
文献类型：
--
作者：
Huang Shanlin;Wang Ming;Zheng Quan;Duan Zhiwen
设α>；0，H=(−Δ)α+V(X)，V(X)属于高阶Kato类K2α(Rn)。对于1≤p≤∞，证明了‖e−i t H(H+M)−β‖L p，L p对所有整数α和2α≥[n2]+1关于时间t的多项式上界，如果α不是整数.与自由情况相比，平滑指数β和t中的增长顺序几乎都是最优的。我们证明的主要内容是半群e−t H的逐点热核估计。我们得到了积分α的具有尖峰系数的高斯上界和分数阶α的多项式衰减性。
Abstract Let α> 0, H=(− Δ) α+ V (x), V (x) belongs to the higher order Kato class K 2 α (R n). For 1≤ p≤∞, we prove a polynomial upper bound of‖ e− i t H (H+ M)− β‖ L p, L p in terms of time t for all integers α and 2 α≥[n 2]+ 1 if α is not an integer. Both the smoothing exponent β and the growth order in t are almost optimal compared to the free case. The main ingredients in our proof are pointwise heat kernel estimates for the semigroup e− t H. We obtain a Gaussian upper bound with sharp coefficient for integral α and a polynomial decay for fractional α.