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In this paper, the parabolic Schrödinger operator $\mathcal{P}={\partial}_t-\triangle+V(x)$ on $\mathbb{R}^{n+1}$ is considered, where $n\ge3,$ nonnegative potential $V$ belongs to the reverse Hölder class $RH_q$ with $q \ge n /2$. The $L^p$ boundedness of operators $V^{\alpha}\mathcal{P}^{-\beta},$ $V^{\alpha}{\nabla}\mathcal{P}^{-\beta}$ and their adjoint operators are established.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2023-0009}, url = {http://global-sci.org/intro/article_detail/ata/24472.html} }In this paper, the parabolic Schrödinger operator $\mathcal{P}={\partial}_t-\triangle+V(x)$ on $\mathbb{R}^{n+1}$ is considered, where $n\ge3,$ nonnegative potential $V$ belongs to the reverse Hölder class $RH_q$ with $q \ge n /2$. The $L^p$ boundedness of operators $V^{\alpha}\mathcal{P}^{-\beta},$ $V^{\alpha}{\nabla}\mathcal{P}^{-\beta}$ and their adjoint operators are established.