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:
![](//static-cambridge-org.ezproxyberklee.flo.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0008439500020191/resource/name/S0008439500020191_eqn01.gif?pub-status=live)
Here V(Dn) is the space of those functions
such that
, where
denotes the characteristic function of a subset E of Dn.