Blasco, Oscar; Karapetyants, Alexey; Restrepo, Joel Holomorphic Hölder-type spaces and composition operators. (English) Zbl 07292717 Math. Methods Appl. Sci. 43, No. 17, 10005-10026 (2020). Summary: We study boundedness and compactness of composition operators in the generalized Hölder-type space of holomorphic functions in the unit disc with prescribed modulus of continuity. We also devote a significant part of the article to outline some embeddings between such Hölder-type spaces, to discuss properties of modulus of continuity and to construct some useful examples. Cited in 5 Documents MSC: 47B33 Linear composition operators 46E15 Banach spaces of continuous, differentiable or analytic functions 30H99 Spaces and algebras of analytic functions of one complex variable Keywords:composition operators; Hölder spaces; holomorphic functions; modulus of continuity PDFBibTeX XMLCite \textit{O. Blasco} et al., Math. Methods Appl. Sci. 43, No. 17, 10005--10026 (2020; Zbl 07292717) Full Text: DOI