CHARACTERIZATION OF NONLINEAR BESOV SPACES

The canonical generalizations of two classical norms on Besov spaces are shown to be equivalent even in the case of nonlinear Besov spaces, that is, function spaces consisting of functions taking values in a metric space and equipped with some Besov-type topology. The proofs are based on atomic decomposition techniques and metric embeddings. Additionally, we provide embedding results showing how nonlinear Besov spaces embed in nonlinear p-variation spaces, and vice versa. We emphasize that we assume neither the unconditional martingale difference property of the involved spaces nor their separability.