# Complex interpolation of vanishing Morrey spaces

## TL;DR

This paper characterizes the complex interpolation properties of vanishing Morrey spaces, clarifies their relation to other function spaces, and demonstrates differences through examples.

## Contribution

It provides the first and second complex interpolation descriptions for vanishing Morrey spaces and establishes their equivalence with certain diamond subspaces.

## Key findings

- Complex interpolation of vanishing Morrey spaces is fully described.
- The diamond subspace and a specific vanishing Morrey space are shown to be identical.
- Examples illustrate that different complex interpolations yield distinct spaces.

## Abstract

We give the description of the first and second complex interpolation of vanishing Morrey spaces, introduced in \cite{AS, CF}. In addition, we show that the diamond subspace (see \cite{HNS}) and one of the function spaces in \cite{AS} are the same. We also give several examples for showing that each of the complex interpolation of these spaces is different.