Every rearrangement-invariant quasi-Banach function space is an interpolation space between two Lorentz spaces

TL;DR

This paper demonstrates that any rearrangement-invariant quasi-Banach function space on a non-atomic measure space can be represented as an interpolation space between two Lorentz spaces, extending previous results.

Contribution

It introduces a method to express any such space as an interpolation space between Lorentz spaces using a specifically constructed interpolation functor.

Findings

Every rearrangement-invariant quasi-Banach space can be represented as an interpolation space.

The construction of the interpolation functor is based on the space itself.

Extends previous results of Kwok-Pun Ho.

Abstract

We extend some results of Kwok-Pun Ho. In particular, it will be shown that every rearrangement-invariant quasi-Banach function space E on a totally sigma-finite measure space with a non-atomic measure can be expressed is the form E=F(L(p0,q0),L(p1,q1)) for an interpolation functor F, where the construction of the functor F is given based on the space E itself.