Boundedness of composition operators in holomorphic Hölder type spaces
Blasco O. Karapetyants A. Restrepo J.E.
30 November 2021John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2021#44Issue 1713670 - 13683 pp.
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.
composition operator , holomorphic functions , Hölder spaces , modulus of continuity
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Department of Mathematical Analysis, University of Valencia, Valencia, Spain
Institute of Mathematics, Mechanic and Computer Sciences and Regional Mathematical Center, Southern Federal University, Rostov-on-Don, Russian Federation
Institute of Mathematics, University of Antioquia, Medellin, Colombia
Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Mathematical Analysis
Institute of Mathematics
Institute of Mathematics
Department of Mathematics
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