On Besov spaces modelled on Zygmund spaces

Working on the dd-torus, we show that Besov spaces Bps(Lp(logL)a) modelled on Zygmund spaces can be described in terms of classical Besov spaces. Several other properties of spaces Bps(Lp(logL)a) are also established. In particular, in the critical case s=d/ps=d/p, we characterize the embedding of Bpd/p(Lp(logL)a) into the space of continuous functions.