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Bounds for the terms in a harmonic polynomial expansion

  • M. P. ALDRED (a1) and D. H. ARMITAGE (a1)

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 uh, we write ∥u=supB[mid ]u[mid ].

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Bounds for the terms in a harmonic polynomial expansion

  • M. P. ALDRED (a1) and D. H. ARMITAGE (a1)

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