On nuclearity of embeddings between Besov spaces
Let \(\{\phi_j \}^\infty_{j=0}\) be the standard dyadic resolution of unity in \(\mathbb R^n\). Let \(s \in \mathbb R\), \(\alpha \in \mathbb R\) and \(1\leq p,q \leq \infty\). Then \(B^{s, \alpha}_{p,q} (\mathbb R^n)\) collects all \(f\in S'(\mathbb R^n)\) such that \[ \Big( \sum^\infty_{j=0} 2^{jsq} (1+j)^{\alpha q} \big\| F^{-1} \big( \phi_j Ff \big) \, | L_p (\mathbb R^n) \big\|^q \Big)^{1/q} \] is finite. If \(\alpha =0\), then \(B^{s,0}_{p,q} (\mathbb R^n) = B^s_{p,q} (\mathbb R^n)\) are the classical Besov spaces. Let \(B^{s, \alpha}_{p,q} ( \Omega)\) be the restriction of \(B^{s,\alpha}_{p,q} (\mathbb R^n)\) to the bounded Lipschitz domain \(\Omega\) in \(\mathbb R^n\). The paper studies under which conditions for the parameters involved the embedding of \(B^{s_1, \alpha_1}_{p_1, q_1} (\Omega)\) into \(B^{s_2, \alpha_2}_{p_2, q_2} (\Omega)\) is nuclear.
scientific article; zbMATH DE number 6820494
scientific article