Weighted Calder\'on-Hardy spaces

Let $0<p\le 1<q<\mathrm{\infty }$ and $\gamma >0$. In this note we discuss the weighted Calder'on-Hardy spaces on ${\mathbb{R}}^n$, $$\mathcal{H}$^{p}_{q, \gamma}($\mathbb{R}$^{n}, w)$\mathrm{.}For$\gamma = 2m$,$m \in $\mathbb{N}$$,and$n (2m

• n/q)^{-1} < p \leq 1$,weshowthatforcertainpowerweights$w$ the iterated Laplace operator ${\mathrm{\Delta }}^m$ is a bijective mapping from ${\mathcal{H}}_{q,2m}^p({\mathbb{R}}^n,w)$ onto $H^p({\mathbb{R}}^n,w)$.