Wavelet decomposition and embeddings of generalised Besov–Morrey spaces. (January 2022)

• Record Type: Journal Article
• Authors: Haroske, Dorothee D.; Moura, Susana D.; Skrzypczak, Leszek
• Is Part Of: Nonlinear analysis. Volume 214(2022)
• Publication Date: 2022-01
• Subjects: 46E35; Besov–Morrey spaces -- Generalised Morrey spaces -- Embeddings -- Wavelet decompositions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112590
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study embeddings between generalised Besov–Morrey spaces N φ, p, q s ( R d ) . Both sufficient and necessary conditions for the embeddings are proved. Embeddings of the Besov–Morrey spaces into the Lebesgue spaces L r ( R d ) are also considered. Our approach requires a wavelet characterisation of the spaces which we establish for the system of Daubechies wavelets.