Calderón-Hardy type spaces and the Heisenberg sub-Laplacian
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910113602732032 |
|---|---|
| author | Rocha, Pablo |
| author_facet | Rocha, Pablo |
| contents | For $0 < p \leq 1 < q < \infty$ and $γ> 0$, we introduce the Calderón-Hardy spaces $\mathcal{H}^{p}_{q, γ}(\mathbb{H}^{n})$ on the Heisenberg group $\mathbb{H}^{n}$, and show for every $f \in H^{p}(\mathbb{H}^{n})$ that the equation \[ \mathcal{L} F = f \] has a unique solution $F$ in $\mathcal{H}^{p}_{q, 2}(\mathbb{H}^{n})$, where $\mathcal{L}$ is the sublaplacian on $\mathbb{H}^{n}$, $1 < q < \frac{n+1}{n}$ and $(2n+2) \, (2 + \frac{2n+2}{q})^{-1} < p \leq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12163 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Calderón-Hardy type spaces and the Heisenberg sub-Laplacian Rocha, Pablo Classical Analysis and ODEs For $0 < p \leq 1 < q < \infty$ and $γ> 0$, we introduce the Calderón-Hardy spaces $\mathcal{H}^{p}_{q, γ}(\mathbb{H}^{n})$ on the Heisenberg group $\mathbb{H}^{n}$, and show for every $f \in H^{p}(\mathbb{H}^{n})$ that the equation \[ \mathcal{L} F = f \] has a unique solution $F$ in $\mathcal{H}^{p}_{q, 2}(\mathbb{H}^{n})$, where $\mathcal{L}$ is the sublaplacian on $\mathbb{H}^{n}$, $1 < q < \frac{n+1}{n}$ and $(2n+2) \, (2 + \frac{2n+2}{q})^{-1} < p \leq 1$. |
| title | Calderón-Hardy type spaces and the Heisenberg sub-Laplacian |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2505.12163 |