The boundedness of commutators associated with Schrödinger operators on Herz spaces
The boundedness of commutators associated with Schrödinger operators on Herz spaces
Let $L=-\Delta+V$ be a Schrödinger operators on $\mathbb{R}^{n}$ , $n\geq3$ , where the nonnegative potential V belongs to the reverse Hölder class $B_{s}$ for $s>\frac{d}{2}$ . Let $T_{\beta}=(-\Delta +V)^{-\beta}V^{\beta}$ , $\beta>0$ , and $R_{L}=\nabla(-\Delta+V)^{-1/2}$ be the Riesz transform associated to L. We prove that the operator $T_{\beta}$ and $R_{L}$ are …