Hardy spaces, Campanato spaces and higher order Riesz transforms associated with Bessel operators
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916693039644672 |
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| author | Bui, The Anh |
| author_facet | Bui, The Anh |
| contents | Let $ν= (ν_1, \ldots, ν_n) \in (-1/2, \infty)^n$, with $n \ge 1$, and let $Δ_ν$ be the multivariate Bessel operator defined by
\[
Δ_ν = -\sum_{j=1}^n\left( \frac{\partial^2}{\partial x_j^2} - \frac{ν_j^2 - 1/4}{x_j^2} \right).
\]
In this paper, we develop the theory of Hardy spaces and BMO-type spaces associated with the Bessel operator $Δ_ν$. We then study the higher-order Riesz transforms associated with $Δ_ν$. First, we show that these transforms are Calderón-Zygmund operators. We further prove that they are bounded on the Hardy spaces and BMO-type spaces associated with $Δ_ν$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11758 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hardy spaces, Campanato spaces and higher order Riesz transforms associated with Bessel operators Bui, The Anh Classical Analysis and ODEs Let $ν= (ν_1, \ldots, ν_n) \in (-1/2, \infty)^n$, with $n \ge 1$, and let $Δ_ν$ be the multivariate Bessel operator defined by \[ Δ_ν = -\sum_{j=1}^n\left( \frac{\partial^2}{\partial x_j^2} - \frac{ν_j^2 - 1/4}{x_j^2} \right). \] In this paper, we develop the theory of Hardy spaces and BMO-type spaces associated with the Bessel operator $Δ_ν$. We then study the higher-order Riesz transforms associated with $Δ_ν$. First, we show that these transforms are Calderón-Zygmund operators. We further prove that they are bounded on the Hardy spaces and BMO-type spaces associated with $Δ_ν$. |
| title | Hardy spaces, Campanato spaces and higher order Riesz transforms associated with Bessel operators |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2504.11758 |