Bourgain Algebras of Spaces of n-Harmonic Functions in the Unit Polydisk
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AbstractLet 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.
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