Nuclear embeddings of Besov spaces into Zygmund spaces

Abstract

Let d ∈ N and let Ω be a bounded Lipschitz domain in Rd. We prove that the embedding Id : Bd (Ω) −→ L (log L) (Ω) is nuclear if a < −1 and 1 ≤ p, q ≤ ∞,p,q ≤∞, while if −1 < a < 0, 2 < p < ∞ and p ≤ q ≤ ∞ while if −1 < a < 0, 2 < p < ∞ and p ≤ q ≤ ∞ the embedding Id fails to be nuclear. Furthermore, if a = −1, the embedding Id : Bd∞,∞(Ω) −→ L∞ (log L)−1 (Ω) is not nuclear.