Nuclear Embeddings of Besov Spaces into Zygmund Spaces

Let d is an element of N and let Omega be a bounded Lipschitz domain in Rd. We prove that the embedding Id:Bp,qd(Omega)?Lp(logL)a(Omega) is nuclear if a<-1 and 1 <= p,q <=infinity, while if -1<0, 2 <=infinity the embedding Id fails to be nuclear. Furthermore, if a=-1, the embedding Id:B infinity,infinity d(Omega)?L infinity(logL)-1(Omega) is not nuclear.