Heisenberg群上与Schrödinger算子相关的Riesz变换在Hardy空间上的有界性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (1): 46-62.

Heisenberg群上与Schrödinger算子相关的Riesz变换在Hardy空间上的有界性

陈萱()

青岛大学数学与统计学院山东青岛 266071

收稿日期:2019-08-28 出版日期:2021-02-26 发布日期:2021-01-29
作者简介:陈萱, E-mail: cxlyuqdu@163.com
基金资助:
国家自然科学基金(11871293);国家自然科学基金(11571217);山东自然科学基金(ZR2017JL008);山东自然科学基金(ZR2016AM05);山东省高校科技项目(J15LI15)

Boundness of Riesz Transforms on Hardy Spaces Associated with Schrödinger Operators on the Heisenberg Group

Xuan Chen()

School of Mathematics and Statistics, Qingdao University, Shandong Qingdao 266071

Received:2019-08-28 Online:2021-02-26 Published:2021-01-29
Supported by:
Supported by the NSFC(11871293);Supported by the NSFC(11571217);the Shandong Natural Science Foundation(ZR2017JL008);the Shandong Natural Science Foundation(ZR2016AM05);the University Science and Technology Projects of Shandong Province(J15LI15)

摘要/Abstract

摘要：

令 $L=-\Delta_{{\Bbb H}^{n}}+V$ 是Heisenberg群 ${\Bbb H}^{n}$ 上Schrödinger算子，其中非负位势 $V$ 属于逆Hölder类.该文用分子刻画与 $L$ 相关的Hardy型空间 $H^p_L({\Bbb H}^{n})$ ，进而得到了与 $L$ 相关的Riesz变换的 $H_{L}^{p}$ -有界性.

关键词: Hardy空间, Heisenberg群, Riesz变换, Schrödinger算子

Abstract:

Let $L=-\Delta_{{\Bbb H}^{n}}+V$ be a Schrödinger operator on the Heisenberg group ${\Bbb H}^{n}$ , where $V$ is a nonnegative potential belonging to the reverse Hölder class. By the molecular decomposition of the Hardy space $H_{L}^{p}({\Bbb H}^{n})$ , we obtain the $H^p_L$ -boundedness of the Riesz transform associated with $L$ .

Key words: Hardy spaces, Heisenberg group, Riesz transform, Schrö dinger operators

中图分类号:

O174.2

陈萱. Heisenberg群上与Schrödinger算子相关的Riesz变换在Hardy空间上的有界性[J]. 数学物理学报, 2021, 41(1): 46-62.

Xuan Chen. Boundness of Riesz Transforms on Hardy Spaces Associated with Schrödinger Operators on the Heisenberg Group[J]. Acta mathematica scientia,Series A, 2021, 41(1): 46-62.

参考文献 11

1	Dong J F , Huang J Z , Liu H P . Boundedness of singular integrals on Hardy type spaces associated with Schrödinger operators. Journal of Function Spaces, 2015, 2015: 1- 11
2	Fefferman C L . The uncertainty principle. Bulletin of the American Mathematical Society, 1983, 9 (2): 129- 206 doi: 10.1090/S0273-0979-1983-15154-6
3	Goldstein J A . Semigoups of Linear Operators and Applications New York: Oxford University Press, 1985
4	Li P T , Peng L Z . L^p boundedness of commutator operator associated with Schrödinger operators on Heisenberg group. Acta Mathematica Scientia, 2012, 32 (2): 568- 578 doi: 10.1016/S0252-9602(12)60039-3
5	Lin C C , Liu H P . BMO_L( ${\Bbb H}^{n}$ ) spaces and Carleson measures for Schrödinger operators. Advances in Mathematics, 2011, 228 (3): 1631- 1688 doi: 10.1016/j.aim.2011.06.024
6	Lin C C, Liu H P, Liu Y. Hardy spaces associated with Schrödinger operators on the Heisenberg group. 2011, arXiv: 1106.4960
7	Liu Y , Tang G B . A note for Riesz transforms associated with Schrödinger operator on the Heisenberg group. Analysis and Mathematical Physics, 2017, 7 (1): 31- 45 doi: 10.1007/s13324-016-0128-6
8	Lu G Z . A Fefferman-Phong type inequality for degenerate vector fields and applications. Panamerican Mathematical Journal, 1996, 6 (4): 37- 57
9	Shen Z W . L^p estimates for Schrödinger operators with certain potentials. Annales Institut Fourier, 1995, 45 (2): 513- 546 doi: 10.5802/aif.1463
10	Wang Y X , Li P T . Riesz transforms on the Hardy space associated with generalized Schrödinger operators. Journal of Inequalities and Applications, 2019, 2019 (1): 1- 20 doi: 10.1186/s13660-019-1955-4
11	Zhong J P. Harmonic Analysis for Some Schrödinger type Operators[D]. Princeton: Princeton University, 1993

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