Associate spaces of logarithmic interpolation spaces and generalized Lorentz–Zygmund spaces

Abstract

We determine the associate space of the logarithmic interpolation space (X0, X1)1,q,A where X0 and X1 are Banach function spaces over a σ-finite measure space (Ω, µ). Particularizing the results for the case of the couple (L1, L∞) over a non-atomic measure space, we recover results of Opic and Pick on associate spaces of generalized Lorentz-Zygmund spaces L(∞,q;A). We also establish the corresponding results for sequence spaces.