@Article{Rocha2026,
author = "Rocha, Pablo",
title = "Calderón-Hardy type spaces and the Heisenberg sub-Laplacian",
journal = "Opuscula Math.",
year = "2026",
volume = "46",
number = "1",
pages = "73--99",
doi = "https://doi.org/10.7494/OpMath.202512221",
url = "https://doi.org/10.7494/OpMath.202512221",
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",
issn = "1232-9274"
}