Complex interpolation of smoothness Triebel-Lizorkin-Morrey spaces

This paper extends the result in \cite{HNS15} to Triebel-Lizorkin-Morrey spaces which contains $4$ parameters $p,q,r,s$. This paper reinforces our earlier paper \cite{HNS15} by Nakamura, the first and the third authors in two different directions. First, we include the smoothness parameter $s$ and the second smoothness parameter $r$. In \cite{HNS15} we assumed $s=0$ and $r=2$. Here we relax the conditions on $s$ and $r$ to $s \in {\mathbb R}$ and $1 < r \le \infty$. Second, we apply a formula obtained by Bergh in 1978 to prove our main theorem without using the underlying sequence spaces.