TY - JOUR
T1 - Estimates for Parabolic Schrödinger Operators with Certain Nonnegative Potentials
AU - Wang , Yanhui
JO - Analysis in Theory and Applications
VL - 3
SP - 197
EP - 207
PY - 2025
DA - 2025/09
SN - 41
DO - http://doi.org/10.4208/ata.OA-2023-0009
UR - https://global-sci.org/intro/article_detail/ata/24472.html
KW - $L^p$ estimate, parabolic Schrödinger operator, reverse Hölder class.
AB - <p style="text-align: justify;">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.</p>