Some estimates for commutators of Riesz transform associated with Schrödinger type operators
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- 作者：Yu Liu ; Jing Zhang ; Jie-Lai Sheng ; Li-Juan Wang
- 关键词：commutator ; Hardy space ; reverse Hölder inequality ; Riesz transform ; Schrödinger operator ; Schrödinger type operator
- 刊名：Czechoslovak Mathematical Journal
- 出版年：2016
- 出版时间：March 2016
- 年：2016
- 卷：66
- 期：1
- 页码：169-191
- 全文大小：227 KB
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[19] J. Zhong: Harmonic Analysis for some Schrödinger Type Operators. Ph. D. Thesis, Princeton University, 1993. - 作者单位：Yu Liu (1)
Jing Zhang (1)
Jie-Lai Sheng (1)
Li-Juan Wang (1)
1. School of Mathematics and Physics, University of Science and Technology Beijing, No. 30 Xueyuan Road, Haidian, Beijing, 100083, P.R. China - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics
Analysis
Convex and Discrete Geometry
Ordinary Differential Equations
Mathematical Modeling and IndustrialMathematics - 出版者：Springer Netherlands
- ISSN：1572-9141
文摘
Let L 1 = −Δ + V be a Schr:dinger operator and let L 2 = (−Δ)2 + V 2 be a Schrödinger type operator on ℝ n (n ⩾ 5), where V≠ 0 is a nonnegative potential belonging to certain reverse Hölder class B s for s ⩾ n/2. The Hardy type space \(H_{{L_2}}^1\) is defined in terms of the maximal function with respect to the semigroup \(\left\{ {{e^{ - t{L_2}}}} \right\}\) and it is identical to the Hardy space \(H_{{L_1}}^1\) established by Dziubański and Zienkiewicz. In this article, we prove the L p -boundedness of the commutator R b = bRf - R(bf) generated by the Riesz transform \(R = {\nabla ^2}L_2^{ - 1/2}\), where \(b \in BM{O_\theta }(\varrho )\), which is larger than the space BMO(ℝ n ). Moreover, we prove that R b is bounded from the Hardy space \(H_{\mathcal{L}_1 }^1 \) into weak \(L_{weak}^1 (\mathbb{R}^n )\).