Real Interpolation for mixed Lorentz spaces and Minkowski's inequality

TL;DR

This paper investigates the properties of real interpolation spaces between mixed Lorentz spaces, establishing embeddings and identities, and explores Minkowski's inequality in Lorentz spaces under optimal conditions.

Contribution

It provides new embeddings and identities for real interpolation spaces between mixed Lorentz spaces and clarifies Minkowski's inequality conditions in these spaces.

Findings

Established embeddings and identities for real interpolation spaces

Derived optimal conditions for Minkowski's inequality in Lorentz spaces

Enhanced understanding of the structure of mixed Lorentz spaces

Abstract

We prove embeddings and identities for real interpolation spaces between mixed Lorentz spaces. This partly relies on Minkowski's (reverse) integral inequality in Lorentz spaces $L^{p,r}(X)$ under optimal assumptions on the exponents $(p,r)\in (0,\infty)\times (0,\infty]$.