Calderón-Hardy spaces on the Heisenberg group and the solution of the equation $\mathcal{L} F = f$ for $f \in H^p(\mathbb{H}^n)$

Abstract: For $0 &lt; p \leq 1 &lt; q &lt; \infty$ and $\gamma &gt; 0$, we introduce the Calder\'on-Hardy spaces $$\mathcal{H}^{p}_{q, \gamma}(\mathbb{H}<sup>{n})$$ on the Heisenberg group $\mathbb{H}<sup>{n}$, and show for every $f \in H<sup>{p}(\mathbb{H}<sup>{n})$ that the equation [ \mathcal{L} F = f ] has a unique solution $F$ in $$\mathcal{H}^{p}_{q, 2}(\mathbb{H}<sup>{n})$$, where $\mathcal{L}$ is the sublaplacian on $\mathbb{H}<sup>{n}$, $1 &lt; q &lt; \frac{n+1}{n}$ and $(2n+2) \, (2 + \frac{2n+2}{q})^{-1} &lt; p \leq 1$.