Beurling’s Minimum Principle in a Cone

This paper shows that some characterizations of the harmonic majorization of the Martin function connected with adomain having smooth boundary without acorner e.g aball and a half-space also hold for aspecial domain with corners, i.e. acone. 1. Introduction. Let $\mathrm{R} $ and $\mathrm{R}_{+} $ be the set of all real numbers and all positive real numbers, respectively. We denote by $\mathrm{R}^{n}(n\geq 2) $ the $\mathrm{n}$-dimensional Euclidean space. Apoint in $\mathrm{R}^{n} $ is denoted by $P=(X, y),X=(x_{1}, x_{2}, \ldots, x_{n-1}) $. The Euclidean distance of two points $P $ and $Q $ in $\mathrm{R}^{n} $ is denoted by $|P-Q| $. Also $|P-O| $ with the origin $O $ of $\mathrm{R}^{n} $ is simply denoted by $|P| $