Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 607–623

THE CHARACTERIZATIONS OF HARDY–SOBOLEV SPACES BY FRACTIONAL SQUARE FUNCTIONS RELATED TO SCHRÖDINGER OPERATORS

Jizheng Huang, Pengtao Li, Yu Liu and Jie Xin

Beijing University of Posts and Telecommunications, School of Science
Beijing 100876, P.R. China; hjzheng 'at' 163.com

Qingdao University, College of Mathematics
Qingdao, Shandong 266071, P.R. China; ptli 'at' qdu.edu.cn

University of Science and Technology Beijing, School of Mathematics and Physics
Beijing 100083, P.R. China; liuyu75 'at' pku.org.cn

Qufu Normal University, School of Mathematical Sciences
Qufu 273165, P.R. China; fdxinjie 'at' sina.com

Abstract. Let L = –Δ + V be a Schrödinger operator, where the potential V satisfies the reverse H\"older condition. In this paper, via the heat semigroup e^–tL and the Poisson semigroup e^–t√L, we introduce several classes of fractional square functions associated with L including the Litttlewood–Paley g-function, the area integral and the g_λ*-function, respectively. By the regularities of semigroup, we establish several square function characterizations of the Hardy space and the Hardy–Sobolev space related to the Schrödinger operator.

2010 Mathematics Subject Classification: Primary 42B35, 47A60, 42B25.

Key words: Hardy space, Hardy–Sobolev spaces, Schrödinger operator, fractional square functions.

Reference to this article: J. Huang, P. Li, Y. Liu and J. Xin: The characterizations of Hardy–Sobolev spaces by fractional square functions related to Schrödinger operators. Ann. Acad. Sci. Fenn. Math. 45 (2020), 607–623.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4530