Abstract
We work with spaces (A0,A1)θ,q,A which are logarithmic perturbations of the real interpolation spaces. We determine the dual of (A0,A1)θ,q,A when 0<q<1. As we show, if θ=0 or 1 then the dual space depends on the relationship between q and A. Furthermore we apply the abstract results to compute the dual space of Besov spaces of logarithmic smoothness and the dual space of spaces of compact operators in a Hilbert space which are close to the Macaev ideals.
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