Entropy numbers of embeddings of some 2-microlocal Besov spaces

We investigate compactness and asymptotic behaviour of the entropy numbers of embeddings Bp1,q1s1,s1′(Rn,U)↪Bp2,q2s2,s2′(Rn,U). Here Bp,qs,s′(Rn,U) denotes a 2-microlocal Besov space with a weight given by the distance to a fixed set U⊂RnU⊂Rn.