Sharp semiclassical spectral asymptotics for Schrödinger operators with non-smooth potentials

We consider semiclassical Schrödinger operators acting in $L^2({\mathbb{R}}^d)$ with $d\ge 3$. For these operators we establish a sharp spectral asymptotics without full regularity. For the counting function we assume the potential is locally integrable and that the negative part of the potential minus a constant is one time differentiable and the derivative is Hölder continues with parameter $\mu \ge 1\mathrm{/}2$. Moreover we also consider sharp Riesz means of order $\gamma$ with $\gamma \in (0,1]$. Here we assume the potential is locally integrable and that the negative part of the potential minus a constant is two time differentiable and the second derivative is Hölder continues with parameter $\mu$ that depends on $\gamma$.