Boundedness of composition operators in holomorphic Hölder type spaces

Óscar Blasco, Alexey Nikolaevich Karapetyants, Joel Esteban Restrepo

2021

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DOI 10.1002/mma.7650
Data confidence 70 medium
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Abstract

A new characterization of boundedness of the composition operators in generalized Hölder spaces is obtained in terms that do not use the derivative of the composition operator, but using some averaging construction which represents certain integration of the modulus of continuity involving the symbol of the composition operator. This approach also allows to recover previously known results for the standard weights ω(t) = tα with 0 < α < 1. Certain further results on characterization of the same spaces are obtained as well.