Embeddings of Besov spaces of logarithmic smoothness

Abstract

This paper deals with Besov spaces of logarithmic smoothness B-p,T(0,b) formed by periodic functions. We study embeddings of B-p,T(0,b) into Lorentz-Zygmund spaces L-p,L-q(log L)(beta). Our techniques rely on the approximation structure of B-p,T(0,b), Nikol'skii type inequalities, extrapolation properties of L-p,L-q(log L)(beta) and interpolation.