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

Published online by Cambridge University Press:  20 November 2018

Keiji Izuchi
Affiliation:
Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-21, Japan
Kazuhiro Kasuga
Affiliation:
Department of Mathematics, Faculty of Science, Shinshu University, Matsumoto 390, Japan
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Abstract

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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 .

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1996

References

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