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For the classical space of functions with bounded mean oscillation, it iswell known that VMO** = BMO and there are many characterizations of thedistance from a function f in BMO to VMO. When considering the Bloch space,results in the same vein are available with respect to the little Bloch space.In this paper such duality results and distance formulas are obtained by purefunctional analysis. Applications include general M\"obius invariant spacessuch as Q_K-spaces, weighted spaces, Lipschitz-H\"older spaces and rectangularBMO of several variables.

Duality and Distance Formulas in Spaces Defined by Means of Oscillation