Let h∞(Dn) denote the space of all bounded n-harmonic functions on the unit polydisk Dn of Cn. In this paper we prove that the Bourgain algebra h∞(Dn)b and h∞(Dn)bb relative to the Lebesgue space L∞(Dn) are of the following forms:

Here V(Dn) is the space of those functions
such that
, where
denotes the characteristic function of a subset E of Dn.