On potentials of distributions in Orlicz-Hardy type spaces on the Heisenberg group
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914594264449024 |
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| author | Rocha, Pablo |
| author_facet | Rocha, Pablo |
| contents | In this work, we introduce Orlicz-Hardy type spaces and Orlicz-Calderón Hardy type spaces on the Heisenberg group $\mathbb{H}^{n}$ and study the relationship between them by means of the Heisenberg sub-Laplacian $\mathcal{L}$. More precisely, we show, under suitable assumptions, that every distribution in the Orlicz-Hardy space $H^Φ(\mathbb{H}^{n})$ can be represented uniquely as the sub-Laplacian of a function in an appropriate Orlicz-Calderón Hardy space. In this way, for any $f \in H^Φ(\mathbb{H}^{n})$, we obtain a uniqueness and solvability result for the equation $\mathcal{L}F=f$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_24194 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On potentials of distributions in Orlicz-Hardy type spaces on the Heisenberg group Rocha, Pablo Classical Analysis and ODEs In this work, we introduce Orlicz-Hardy type spaces and Orlicz-Calderón Hardy type spaces on the Heisenberg group $\mathbb{H}^{n}$ and study the relationship between them by means of the Heisenberg sub-Laplacian $\mathcal{L}$. More precisely, we show, under suitable assumptions, that every distribution in the Orlicz-Hardy space $H^Φ(\mathbb{H}^{n})$ can be represented uniquely as the sub-Laplacian of a function in an appropriate Orlicz-Calderón Hardy space. In this way, for any $f \in H^Φ(\mathbb{H}^{n})$, we obtain a uniqueness and solvability result for the equation $\mathcal{L}F=f$. |
| title | On potentials of distributions in Orlicz-Hardy type spaces on the Heisenberg group |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2605.24194 |