The Marcel Riesz Kernel and a Green Kernel for a Half-Space

Abstract

<p>The principal object of this thesis is to study some aspects of the Marcel Riesz kernel and the notion of superharmonicity of fractional order. We define a Green kernel for a half-space and show that this kernel satisfies the principle of domination. This lead us to a new definition of superharmonicity of fractional order on a half-space.</p>