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Molecular decomposition and Fourier multipliers for holomorphic Besov and Triebel–Lizorkin spaces

  • G. Cleanthous
  • A. G. Georgiadis
  • M. NielsenEmail author
Article
  • 29 Downloads

Abstract

Smooth molecular decompositions for holomorphic Besov and Triebel–Lizorkin spaces on the unit disk of the complex plane are constructed. The decompositions are used to obtain a boundedness result for Fourier multipliers. As further applications, we provide equivalent norms for the spaces under consideration, we consider the implications of the results on Hardy and Hardy–Sobolev spaces, and we study boundedness of coefficient multipliers.

Keywords

Besov spaces Distributions Fourier multipliers Hardy spaces Hardy–Sobolev spaces Holomorphic functions Molecular decomposition Triebel–Lizorkin spaces 

Mathematics Subject Classification

30H25 42A16 (primary) and 30B30 30B40 30H10 42A05 42A45 (secondary) 

Notes

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CyprusNicosiaCyprus
  2. 2.Department of Mathematical SciencesAalborg UniversityAalborg EastDenmark

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