$L^p$ Estimates for Higher-Order Parabolic Schrödinger Operators with Certain Nonnegative Potentials
Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 1
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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} $.
Classification :
35J10, 35K25
@article{BMMS_2014_37_1_a14,
author = {Yu Liu and Jizheng Huang and Jianfeng Dong},
title = {$L^p$ {Estimates} for {Higher-Order} {Parabolic} {Schr\"odinger} {Operators} with {Certain} {Nonnegative} {Potentials}},
journal = {Bulletin of the Malaysian Mathematical Society},
year = {2014},
volume = {37},
number = {1},
url = {http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a14/}
}
TY - JOUR AU - Yu Liu AU - Jizheng Huang AU - Jianfeng Dong TI - $L^p$ Estimates for Higher-Order Parabolic Schrödinger Operators with Certain Nonnegative Potentials JO - Bulletin of the Malaysian Mathematical Society PY - 2014 VL - 37 IS - 1 UR - http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a14/ ID - BMMS_2014_37_1_a14 ER -
%0 Journal Article %A Yu Liu %A Jizheng Huang %A Jianfeng Dong %T $L^p$ Estimates for Higher-Order Parabolic Schrödinger Operators with Certain Nonnegative Potentials %J Bulletin of the Malaysian Mathematical Society %D 2014 %V 37 %N 1 %U http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a14/ %F BMMS_2014_37_1_a14
Yu Liu; Jizheng Huang; Jianfeng Dong. $L^p$ Estimates for Higher-Order Parabolic Schrödinger Operators with Certain Nonnegative Potentials. Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a14/