Abstract
Let and |zz t |<1} be the Lie ball in ℂ2 and let ℋ be the associated Hua operator. Then, for a complex number λ such that ℛe(iλ)>0, we establish that every ℂ-valued function F on 𝒟2 satisfying the following Hua system of differential equations is the Poisson transform of an L 2-function on the Shilov boundary S of 𝒟2 if and only if it satisfies the following growth condition of Hardy type:
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