Abstract: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 $H^{\Phi}(\mathbb{H}^{n})$ can be represented uniquely as the sub-Laplacian of a function in an appropriate Orlicz-Calderón Hardy space. In this way, for any $f \in H^{\Phi}(\mathbb{H}^{n})$, we obtain a uniqueness and solvability result for the equation $\mathcal{L}F=f$.
| Comments: | 28 pages |
| Subjects: | Classical Analysis and ODEs (math.CA) |
| Cite as: | arXiv:2605.24194 [math.CA] |
| (or arXiv:2605.24194v1 [math.CA] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24194 arXiv-issued DOI via DataCite (pending registration) |
From: Pablo Rocha [view email]
[v1]
Fri, 22 May 2026 20:33:43 UTC (21 KB)
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