Opuscula Math. 46, no. 1 (2026), 73-99
https://doi.org/10.7494/OpMath.202512221
Opuscula Mathematica
Calderón-Hardy type spaces and the Heisenberg sub-Laplacian
Abstract. For \(0 \lt p \leq 1 \lt q \lt \infty\) and \(\gamma \gt 0\), we introduce the Calderón-Hardy spaces \(\mathcal{H}^{p}_{q,\gamma}(\mathbb{H}^{n})\) 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 sub-Laplacian on \(\mathbb{H}^{n}\), \[1 \lt q \lt \frac{n+1}{n} \quad \text{and} \quad (2n+2)\left(2+\frac{2n+2}{q}\right)^{-1} \lt p \leq 1.\]
Keywords: Calderón-Hardy type spaces, Hardy type spaces, atomic decomposition, Heisenberg group, sub-Laplacian.
Mathematics Subject Classification: 42B25, 42B30, 42B35, 43A80.
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- Pablo Rocha
- Universidad Nacional del Sur, Departamento de Matemática, Avenida Alem 1253. 2do Piso, 8000 Bahía Blanca, Argentina
- Communicated by Palle E.T. Jorgensen.
- Received: 2025-05-12.
- Revised: 2025-12-22.
- Accepted: 2025-12-22.
- Published online: 2026-01-27.
