Complex interpolation of various subspaces of Morrey spaces

Abstract

In this article, we discuss the complex interpolation of various closed subspaces of Morrey spaces. We have been considering some closed subspaces of Morrey spaces in our earlier works. The main property that we need is the lattice property but in connection with the diamond spaces defined by Yuan et al. (2015), it seems to be natural to consider the convolution property as well. Our result will extend the results by Hakim and Sawano (2017) and Hakim et al. (2017).