On nuclearity of embeddings between Besov spaces

Let B-p,q(s,alpha)(Omega) be the Besov space with classical smoothness s and additional logarithmic smoothness of order alpha on a bounded Lipschitz domain Omega in R-d. For s(1), s(2) is an element of 1 <= p(1), p(2), q(1), q(2) <= infinity and s(1) - s(2) = d - d(1/p(2) - 1/p(1))+, we show a sufficient condition on q(1), q(2) for nuclearity of embedding B-p1,q1(s1,alpha 1) (Omega) hooked right arrow B-p2,q2(s2,alpha 2) (Omega) We also show that the condition is necessary in a wide range of parameters. (C) 2017 Elsevier Inc. All rights reserved.