Bounds for the terms in a harmonic polynomial expansion
M. P. Aldred, D. H. Armitage · Mathematical Proceedings of the Cambridge Philosophical Society · 1998
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 ].