Weighted Calderón-Hardy spaces

Abstract

We present the weighted Calderón-Hardy spaces on Euclidean spaces and investigate their properties. As an application we show, for certain power weights, that the iterated Laplace operator is a bijection from these spaces onto classical weighted Hardy spaces. The main tools to achieve our result are an atomic decomposition of weighted Hardy spaces furnished by the author, fundamental solutions of iterated Laplacian and pointwise inequalities for certain maximal functions.

Keywords

• weighted calderón-hardy space
• weighted hardy space
• atomic decomposition
• laplace operator