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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2504.09867 |
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| _version_ | 1866913791918211072 |
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| author | Bui, The Anh Duong, Xuan Thinh |
| author_facet | Bui, The Anh Duong, Xuan Thinh |
| contents | Let \(\mathcal{L}_ν\) be the Laguerre differential operator which is the self-adjoint extension of the differential operator \[ L_ν:= \sum_{i=1}^n \left[-\frac{\partial^2}{\partial x_i^2} + x_i^2 + \frac{1}{x_i^2} \left(ν_i^2 - \frac{1}{4} \right) \right] \] initially defined on \(C_c^\infty(\mathbb{R}_+^n)\) as its natural domain, where \(ν\in [-1/2,\infty)^n\), \(n \geq 1\). In this paper, we first develop the theory of Hardy spaces \(H^p_{\mathcal{L}_ν}\) associated with \(\mathcal{L}_ν\) for the full range \(p \in (0,1]\). Then we investigate the corresponding BMO-type spaces and establish that they coincide with the dual spaces of \(H^p_{\mathcal{L}_ν}\). Finally, we show boundedness of higher-order Riesz transforms on Lebesgue spaces, as well as on our new Hardy and BMO-type spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09867 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hardy spaces and Campanato spaces associated with Laguerre expansions and higher order Riesz transforms Bui, The Anh Duong, Xuan Thinh Classical Analysis and ODEs Let \(\mathcal{L}_ν\) be the Laguerre differential operator which is the self-adjoint extension of the differential operator \[ L_ν:= \sum_{i=1}^n \left[-\frac{\partial^2}{\partial x_i^2} + x_i^2 + \frac{1}{x_i^2} \left(ν_i^2 - \frac{1}{4} \right) \right] \] initially defined on \(C_c^\infty(\mathbb{R}_+^n)\) as its natural domain, where \(ν\in [-1/2,\infty)^n\), \(n \geq 1\). In this paper, we first develop the theory of Hardy spaces \(H^p_{\mathcal{L}_ν}\) associated with \(\mathcal{L}_ν\) for the full range \(p \in (0,1]\). Then we investigate the corresponding BMO-type spaces and establish that they coincide with the dual spaces of \(H^p_{\mathcal{L}_ν}\). Finally, we show boundedness of higher-order Riesz transforms on Lebesgue spaces, as well as on our new Hardy and BMO-type spaces. |
| title | Hardy spaces and Campanato spaces associated with Laguerre expansions and higher order Riesz transforms |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2504.09867 |