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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 ,
Kazuhiro Kasuga  and
Yasuo Matsugu
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.

Keywords

Primary: 32A35Secondary: 46J15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 3 , 01 September 1996 , pp. 284 - 293
Copyright
Copyright © Canadian Mathematical Society 1996

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