On nuclearity of embeddings between Besov spaces

Abstract

Let Bp,qs,α(Ω) be the Besov space with classical smoothness s and additional logarithmic smoothness of order α on a bounded Lipschitz domain Ω in Rd. For s1, s2 ∈ R, 1 ≤ p1, p2, q1, q2 ≤ ∞ and s1 − s2 = d − d(1/p2 − 1/p1)+, we show a sufficient condition on q1, q2 for nuclearity of embedding Bs1,α1 (superíndices) y p1, q1 (subíndices)(Ω) → Bp2,α2 (superíndice) y s2 q,2 (subíndices) (Ω). We also show that the condition is necessary in a wide range of parameters.