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Volume 37 • Number 1 • 2014
• $L^p$ Estimates for Higher-Order Parabolic Schrödinger Operators with Certain Nonnegative Potentials
Yu Liu, Jizheng Huang and Jianfeng Dong

Let ${\partial}/{\partial t}+(-\Delta)^2 +V^2$ be a higher order parabolic Schrödinger operator on $\mathbb{R}^{n+1}$ $ (n\ge 5)$, where the nonnegative potential $V$ belongs to the reverse H\"{o}lder class $B_{q_{_1}}(\mathbb{R}^n)$ for some $q_{_1}>{n}/{2}$. In this paper we obtain the $L^p(\mathbb{R}^{n+1})$ estimates for the operator $∇^4({\partial}/{\partial t}+(-\Delta)^2 +V^2)^{-1} $.

2010 Mathematics Subject Classification: 35J10, 35K25

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