  Special atom spaces have been around for quite awhile since the introduction
of atoms by R. Coifman in his seminal paper who led to another proof that the
dual of the Hardy space $H^1$ is in fact the space of functions of bounded
means oscillations (BMO). Special atom spaces enjoy quite a few attributes of
their own, among which the fact that they have an analytic extension to the
unit disc. Recently, an extension of special atom spaces to higher dimensions
was proposed, making ripe the possible exploration of the above extension in
higher dimensions. In this paper we propose an analytic characterization of
special atom spaces in higher dimensions.
