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Bounds for the terms in a harmonic polynomial expansion

Published online by Cambridge University Press:  01 March 1998

M. P. ALDRED  and
D. H. ARMITAGE
M. P. ALDRED
Affiliation:
Department of Pure Mathematics, The Queen's University of Belfast
D. H. ARMITAGE
Affiliation:
Department of Pure Mathematics, The Queen's University of Belfast
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Abstract

Let u be harmonic on the unit ball B of the Euclidean space ℝn, where n[ges ]2. There exist homogeneous harmonic polynomials uj of degree j such that [sum ]∞j=0uj converges absolutely and locally uniformly to u on B. We refer to the series [sum ]∞j=0uj, which is unique, as the polynomial expansion of u. By h∞ we denote the Hardy class of all bounded harmonic functions on B, and if u∈h∞, we write ∥u∥∞=supB[mid ]u[mid ].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 123 , Issue 2 , March 1998 , pp. 325 - 327
Copyright
Cambridge Philosophical Society 1998

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