Tent Space Approach of Morrey Spaces and Their Application to Duality and Complex Interpolation

Abstract

The aim in this paper is to establish a new duality property of Morrey spaces and to discover the complex interpolation space between Morrey spaces and Lebesgue spaces. For that purpose, a new space $N_{p,q}^s\left({\mathbf{R}}^n\right)$ is introduced by using methods of tent spaces. The space generalizes Morrey spaces and Lebesgue spaces. Furthermore, this scale of spaces is amenable to the complex interpolation space.