Anal. Theory Appl., 30 (2014), pp. 363-368.
Published online: 2014-11
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Let $\mathcal{L}=-\Delta+V$ be the Schrödinger operator on $\mathbb{R}^d$, where $\Delta$ is the Laplacian on $\mathbb{R}^{d}$ and $V\ne0$ 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 $M_{\alpha,v}^{p_1,q_1}$.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n4.3}, url = {http://global-sci.org/intro/article_detail/ata/4500.html} }Let $\mathcal{L}=-\Delta+V$ be the Schrödinger operator on $\mathbb{R}^d$, where $\Delta$ is the Laplacian on $\mathbb{R}^{d}$ and $V\ne0$ 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 $M_{\alpha,v}^{p_1,q_1}$.