Hardy-Sobolev spaces of higher order associated to Hermite operator

Jizheng Huang; Shuangshuang Ying; Jizheng Huang; Shuangshuang Ying

doi:10.3934/cam.2024037

Communications in Analysis and Mechanics

2024, Volume 16, Issue 4: 858-871. doi: 10.3934/cam.2024037

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Hardy-Sobolev spaces of higher order associated to Hermite operator

Jizheng Huang ^,,
Shuangshuang Ying

Key Laboratory of Mathematics and Information Networks(Ministry of Education) and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, P.R.China

Received: 02 January 2024 Revised: 17 October 2024 Accepted: 07 November 2024 Published: 22 November 2024
42B35, 47A60, 32U20

Let $ L = -\Delta+|x|^2 $ be the Hermite operator on $ \mathbb R^{d} $, where $ \Delta $ is the Laplacian on $ \mathbb R^{d} $. In this paper, we will consider the Hardy-Sobolev spaces of higher order associated with $ L $. We also give some new characterizations of the Hardy spaces associated with $ L $.
- Hardy spaces,
- Riesz transform,
- Hardy-Sobolev spaces,
- Hermite operator
Citation: Jizheng Huang, Shuangshuang Ying. Hardy-Sobolev spaces of higher order associated to Hermite operator[J]. Communications in Analysis and Mechanics, 2024, 16(4): 858-871. doi: 10.3934/cam.2024037

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Abstract

Let $ L = -\Delta+|x|^2 $ be the Hermite operator on $ \mathbb R^{d} $, where $ \Delta $ is the Laplacian on $ \mathbb R^{d} $. In this paper, we will consider the Hardy-Sobolev spaces of higher order associated with $ L $. We also give some new characterizations of the Hardy spaces associated with $ L $.

References

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