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We describe the growth of $p$th means, $1<p<\frac{2n-1}{2(n-1)}$, of theinvariant Green potential in the unit ball in $\mathbb{C}^n$ in terms ofsmoothness properties of a measure.  In particular, a criterion of boundedness of $p$th means of the potential isobtained, a result of M. Stoll is generalized.

Growth description of $p$th means of the Green potential in the unit ball