Analyticity of stokes operator in a weighted space $L^p_γ(R^3_+)$

Abstract

In this paper, I tried to show the analiticity of Stokes operator in a weighted space $L^p_{\gamma}({\bf R}^3_+)$.

This paper also showed that the Hodge decomposition holds on the weighted space $L^p(R^3_+)$, and showed the Stein`s multiplier theorem which has a little improvement of the older one. But this paper is not complete for the main part of the theorem does not have proved yet.