DUALITY OF HARDY SPACE WITH BMO ON THE SHILOV BOUNDARY OF THE PRODUCT DOMAIN IN $\mathbb{C}^{2n}$

Abstract

In this paper, we introduce the BMO space via heat kernels on $\widetilde{M}$, where $\widetilde{M} = M_1 \times \cdots \times M_n$ is the Shilov boundary of the product domain in $\mathbb{C}^{2n}$ defined by Nagel and Stein ([16], see also [17]), each $M_i$ is the boundary of a weakly pseudoconvex domain of finite type in $\mathbb{C}^2$ and the vector fields of $M_i$ are uniformly of finite type ([14]). And we prove that it is the dual space of product Hardy space $H^1(\widetilde{M})$ introduced in [11].