Abstract:

In this paper, assume that $L_{1}$ and $L_{2}$ be self-adjoint operators, and the corresponding heat semigroups ${\rm e}^{-tL_{1}}$ and ${\rm e}^{-tL_{2}}$ satisfy off-diagonal estimates of type ($GGE_{p_{0},m}$) for some $p_{0}\in [1,2)$, we introduce the Hardy space $H_{L_{1}, L_{2}}(\mathbb{R}^{n_{1}}\times \mathbb{R}^{n_{2}})$ associated to $L_{1}$ and $L_{2}$ in terms of the area function, and establish the molecular decomposition by using the theory of tent space on product domain.

Key words: area function, product Hardy space, molecular decomposition