Let $0 < p \leq 1 < q < \infty$ and $γ>0$. In this note we discuss the weighted Calderón-Hardy spaces on $\mathbb{R}^{n}$, $\mathcal{H}^{p}_{q, γ}(\mathbb{R}^{n}, w)$. For $γ= 2m$, $m \in \mathbb{N}$, and $n (2m + n/q)^{-1} < p \leq 1$, we show that for certain power weights $w$ the iterated Laplace operator $Δ^{m}$ is a bijective mapping from $\mathcal{H}^{p}_{q, 2m}(\mathbb{R}^{n},w)$ onto $H^{p}(\mathbb{R}^{n}, w)$.

21 pages. arXiv admin note: text overlap with arXiv:1510.08689