The Boundedness of the Commutator for Riesz Potential Associated with Schrödinger Operator on Morrey Spaces (Analysis in Theory and Applications, 2014)
Let $\mathcal{L}=-\Delta+V$ be the Schrödinger operator on $\mathbb{R}^d$, where $\Delta$ is the Laplacian on $\mathbb{R}^{d}$ and $V e0$ is a nonnegative function satisfying the reverse Hölder's inequality. The authors prove that Riesz potential $\mathcal{J}_{\beta}$ and its commutator $[b,\mathcal{J}_{\beta}]$ associated with $\mathcal{L}$ map from $M_{\alpha,v}^{p,q}$ into $M_{\alpha,v}^{p_1,q_1}$.
Keywords: Reverse Hölder class; commutator; Schrödinger operator.