Real interpolation for mixed Lorentz spaces and Minkowski's inequality

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 $(p,r)\in (0,\infty )\times (0,\infty ]$.