Isomorphic classification of $L_{p,q}$-spaces, II

This is a continuation of the papers [Kuryakov-Sukochev, JFA, 2015] and [Sadovskaya-Sukochev, PAMS, 2018], in which the isomorphic classification of $L_{p,q}$, for $1< p<infty$, $1le q<infty$, $p e q $, on resonant measure spaces, has been obtained. The aim of this paper is to give a complete isomorphic classification of $L_{p,q}$-spaces on general $sigma$-finite measure spaces. Towards this end, several new subspaces of $L_{p,q}(0,1)$ and $L_{p,q}(0,infty)$ are identified and studied.