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

Analytic characterization of high dimension weighted special atom spaces