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Holomorphic Hölder‐type spaces and composition operators
Author(s) -
Blasco Oscar,
Karapetyants Alexey,
Restrepo Joel
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6675
Subject(s) - mathematics , holomorphic function , compact space , composition (language) , modulus of continuity , type (biology) , pure mathematics , mathematical analysis , modulus , construct (python library) , space (punctuation) , geometry , computer science , ecology , philosophy , linguistics , biology , programming language , operating system
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.