Variable Calderón-Hardy spaces on the Heisenberg group
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917169127751680 |
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| author | Rocha, Pablo |
| author_facet | Rocha, Pablo |
| contents | Let $\mathbb{H}^{n}$ be the Heisenberg group and $Q = 2n+2$. For $1 < q < \infty$, $γ> 0$ and an exponent function $p(\cdot)$ on $\mathbb{H}^n$, which satisfy log-Hölder conditions, with $0 < p_{-} \leq p_{+} < \infty$, we introduce the variable Calderón-Hardy spaces $\mathcal{H}^{p(\cdot)}_{q, γ}(\mathbb{H}^{n})$, and show for every $f \in H^{p(\cdot)}(\mathbb{H}^{n})$ that the equation \[ \mathcal{L} F = f \] has a unique solution $F$ in $\mathcal{H}^{p(\cdot)}_{q, 2}(\mathbb{H}^{n})$, where $\mathcal{L}$ is the sublaplacian on $\mathbb{H}^{n}$, $1 < q < \frac{n+1}{n}$ and $Q (2 + \frac{Q}{q})^{-1} < \underline{p}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15760 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variable Calderón-Hardy spaces on the Heisenberg group Rocha, Pablo Classical Analysis and ODEs Let $\mathbb{H}^{n}$ be the Heisenberg group and $Q = 2n+2$. For $1 < q < \infty$, $γ> 0$ and an exponent function $p(\cdot)$ on $\mathbb{H}^n$, which satisfy log-Hölder conditions, with $0 < p_{-} \leq p_{+} < \infty$, we introduce the variable Calderón-Hardy spaces $\mathcal{H}^{p(\cdot)}_{q, γ}(\mathbb{H}^{n})$, and show for every $f \in H^{p(\cdot)}(\mathbb{H}^{n})$ that the equation \[ \mathcal{L} F = f \] has a unique solution $F$ in $\mathcal{H}^{p(\cdot)}_{q, 2}(\mathbb{H}^{n})$, where $\mathcal{L}$ is the sublaplacian on $\mathbb{H}^{n}$, $1 < q < \frac{n+1}{n}$ and $Q (2 + \frac{Q}{q})^{-1} < \underline{p}$. |
| title | Variable Calderón-Hardy spaces on the Heisenberg group |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2505.15760 |