Sharp Broken-Power Lorentz Estimates for Fractional Powers of Radial Schrödinger Operators with Inverse-Square Asymptotics

Haochen Liu, Qinghao Yu, Hongyan Zhou

Let $H=-\Delta +V(|x|)$ be a nonnegative radial Schrödinger operator on ${\mathbb{R}}^d$, $d\ge 2$, whose positive harmonic function satisfies $U(r)\simeq r^{-{\sigma }_0}$ for $0<r\le 1$ and $U(r…