Weighted Calderón-Hardy spaces

Abstract

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

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