Calderon's Complex Interpolation of Morrey Spaces

Abstract

In this note we will discuss some results related to complex interpolation of Morrey spaces. We first recall the Riesz-Thorin interpolation theorem in Section 1. After that, we discuss a partial generalization of this theorem in Morrey spaces proved in \cite{St}. We also discuss non-interpolation property of Morrey spaces given in \cite{BRV99, RV}. In Section 3, we recall the definition of Calder\'on's complex interpolation method and the description of complex interpolation of Lebesgue spaces. In Section 4, we discuss the description of complex interpolation of Morrey spaces given in \cite{CPP98, HS2, Lemarie, LYY}. Finally, we discuss the description of complex interpolation of subspaces of Morrey spaces in the last section. This note is a summary of the current research about interpolation of Morrey spaces, generalized Morrey spaces, and their subspaces in \cite{CPP98, HS, HS2, H, H4, Lemarie, LYY}.