Optimal local embeddings of Besov spaces involving only slowly varying smoothness

The aim of the paper is to establish (local) optimal embeddings of Besov spaces Bp,r0,b involving only a slowly varying smoothness b. In general, our target spaces are outside of the scale of Lorentz–Karamata spaces. In particular, we improve results from Caetano et al. (2011), where the targets are (local) Lorentz–Karamata spaces. To derive such results, we apply limiting real interpolation techniques and weighted Hardy-type inequalities.