Estimates for Parabolic Schrödinger Operators with Certain Nonnegative Potentials (Analysis in Theory and Applications, 2025)
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 $V^{α}\mathcal{P}^{-β},$ $V^{α}{ abla}\mathcal{P}^{-β}$ and their adjoint operators are established.