Complex Interpolation of Morrey Spaces

Abstract

In this article, we extend the previous results on the complex interpolation of Morrey spaces to the case when \(0<q \le p<\infty \). We show that the space produced by the first complex interpolation functor \([{\mathcal M}^{p_0}_{q_0},{\mathcal M}^{p_1}_{q_1}]_\theta \) is a subset of the Morrey space \({\mathcal M}^p_q\) and it contains some closed subspaces of \({\mathcal M}^p_q\). Meanwhile, we prove that Morrey spaces are closed under the second complex interpolation functor. We also present the complex interpolation of certain closed subspaces of Morrey spaces.