Abstract
The classical Hadamard three-circles theorem (1896) gives a relation between the maximum absolute values of an analytic function on three concentric circles. More precisely, it asserts that if f is an analytic function in the annulus {Z epsilon C: r(1) < vertical bar z vertical bar < r(2)}, 0 <r(1) < r < r(2) < infinity, and if M(r(1)), M(r(2)), and M(r) are the maxima of f on the three circles corresponding, respectively, to r(1), r(2), and r then
{M(r)}(log r2/r1) <= {M(r(1))}(log) (r2/r) {M(r2)}(log r/r1).
In this paper we introduce a Hadamard's three-hyperballs type theorem in the framework of Clifford analysis. As a concrete application, we obtain an overconvergence property of special monogenic simple series. (C) 2013 Elsevier Inc. All rights reserved.