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Bourgain Algebras of Spaces of n-Harmonic Functions in the Unit Polydisk
Keiji Izuchi, Kazuhiro Kasuga, Yasuo Matsugu
Journal:

Canadian Mathematical Bulletin / Volume 39 / Issue 3 / 01 September 1996

Published online by Cambridge University Press:

20 November 2018, pp. 284-293

Print publication:

01 September 1996
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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.