Orlicz estimates for parabolic Schrödinger operators with non-negative potentials on nilpotent Lie groups

Kelei Zhang; Kelei Zhang

doi:10.3934/math.2023949

AIMS Mathematics

2023, Volume 8, Issue 8: 18631-18648. doi: 10.3934/math.2023949

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Research article

Orlicz estimates for parabolic Schrödinger operators with non-negative potentials on nilpotent Lie groups

Kelei Zhang ^,

Guangxi Key Laboratory of Cryptography and Information Security, School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China

Received: 21 March 2023 Revised: 16 May 2023 Accepted: 22 May 2023 Published: 02 June 2023
MSC : 35J10, 46E30, 49N60

In this paper, we study the Orlicz estimates for the parabolic Schrödinger operator

$ L = {\partial _t} - {\Delta _X} + V, $

where the nonnegative potential $ V $ belongs to a reverse Hölder class on nilpotent Lie groups $ {\Bbb G} $ and $ {\Delta _X} $ is the sub-Laplace operator on $ {\Bbb G} $. Under appropriate growth conditions of the Young function, we obtain the regularity estimates of the operator $ L $ in the Orlicz space by using the domain decomposition method. Our results generalize some existing ones of the $ L^{p} $ estimates.
- nilpotent Lie group,
- Orlicz space,
- parabolic Schrödinger operator,
- non-negative potential,
- domain decomposition method
Citation: Kelei Zhang. Orlicz estimates for parabolic Schrödinger operators with non-negative potentials on nilpotent Lie groups[J]. AIMS Mathematics, 2023, 8(8): 18631-18648. doi: 10.3934/math.2023949

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Abstract

In this paper, we study the Orlicz estimates for the parabolic Schrödinger operator

$ L = {\partial _t} - {\Delta _X} + V, $

where the nonnegative potential $ V $ belongs to a reverse Hölder class on nilpotent Lie groups $ {\Bbb G} $ and $ {\Delta _X} $ is the sub-Laplace operator on $ {\Bbb G} $. Under appropriate growth conditions of the Young function, we obtain the regularity estimates of the operator $ L $ in the Orlicz space by using the domain decomposition method. Our results generalize some existing ones of the $ L^{p} $ estimates.

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