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Generalized Hölder Spaces of Holomorphic Functions in Domains in the Complex Plane

  • Alexey KarapetyantsEmail author
  • Stefan Samko
Article

Abstract

We study some nonstandard spaces of functions holomorphic in domains on the complex plain with certain smoothness conditions up to the boundary. The first type is the space of Hölder-type holomorphic functions with prescribed modulus of continuity \(\omega =\omega (h)\), and the second is the variable exponent holomorphic Hölder space with the modulus of continuity \(|h|^{\lambda (z)}\). We give a characterization of functions in these spaces in terms of the behavior of their derivatives near the boundary.

Keywords

Hölder spaces holomorphic functions variable exponent spaces modulus of continuity 

Mathematics Subject Classification

30H20 46E30 46E15 

Notes

Acknowledgements

The study was supported by the Grant 18-01-00094-A of the Russian Foundation of Basic Research.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.State University of New YorkAlbanyUSA
  2. 2.Southern Federal UniversityRostov-on-DonRussia
  3. 3.University of AlgarveFaroPortugal

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