Multi-parameter local Hardy spaces (Q2312551)

The authors investigate the bi-parameter local Hardy space theory. By establishing a bi-parameter local reproducing formula, the bi-parameter local Hardy space $h^p(\mathbb{R}^{n_{1}}\times \mathbb{R}^{n_{2}})$ is introduced. They establish the atomic decomposition of the bi-parameter local Hardy spaces. As an application, the authors prove the boundedness from $h^p(\mathbb{R}^{n_{1}}\times \mathbb{R}^{n_{2}})$ to $L^p(\mathbb{R}^{n_{1}+n_{2}})$ of the bi-parameter singular integral operators in the inhomogeneous Journé class for $p$ near 1. All of the results in this paper hold for other multi-parameter setting.