On nuclearity of embeddings between Besov spaces
type: Item
instance of: scholarly article
title: On nuclearity of embeddings between Besov spaces
zbMATH Open document ID: 1386.46034
author: Fernando Cobos
author: Thomas Kühn
author: Óscar Domínguez
published in: Journal of Approximation Theory
publication date: 2017-12-20T00:00:00Z
full work available at URL: Fernando110libre.pdf
review text: 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.
reviewed by: Hans Triebel
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 6820494
zbMATH Keywords: Besov spaces
zbMATH Keywords: nuclear embeddings
zbMATH Keywords: generalized smoothness
MaRDI profile type: Publication
OpenAlex ID: W2767248681
cites work: Wavelet bases in generalized Besov spaces
cites work: Q4112938
cites work: Q3790100
cites work: Approximation and entropy numbers in Besov spaces of generalized smoothness
cites work: Description of logarithmic interpolation spaces by means of the \(J\)-functional and applications
cites work: Q4850055
cites work: Nuclearity and non-nuclearity of some Sobolev embeddings on domains
cites work: Real Interpolation with Logarithmic Functors and Reiteration
cites work: Produits tensoriels topologiques et espaces nucléaires
cites work: A function parameter in connection with interpolation of Banach spaces.
cites work: Q3772707
cites work: Eigenvalue distribution of compact operators
cites work: Q4508978
cites work: Q3336223
cites work: Q5624212
cites work: Q4183861
cites work: Q4722695
cites work: Interpolationstheorie für Banachideale von beschränkten linearen Operatoren
cites work: On Restrictions and Extensions of the Besov and Triebel-Lizorkin Spaces with Respect to Lipschitz Domains
cites work: Diagonal Nuclear Operators on l p Spaces
cites work: Q4169288
cites work: Q3336199
cites work: Q4003552
cites work: Q2731784
cites work: Q5481429
cites work: Function spaces and wavelets on domains
DOI: 10.1016/J.JAT.2017.10.009
description: scientific article; zbMATH DE number 6820494