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Integrability of Mean Oscillation with Applications to Hankel Operators

  • Xiaofen Lv
  • Kehe ZhuEmail author
Article
  • 11 Downloads

Abstract

We introduce and study a family of Banach spaces \(IMO^{s,\sigma }_p\) of functions on the open unit ball \({\mathbb {B}}_n\) in \({\mathbb {C}}^n\), defined by an integrability condition of the mean oscillation in the Bergman metric. Our main results include a decomposition theorem for \(IMO^{s,\sigma }_p\), a characterization of holomorphic functions in \(IMO^{s,\sigma }_p\), and an application of \(IMO^{s,\sigma }_p\) to the boundedness and compactness of Hankel operators between weighted Bergman spaces.

Keywords

Bergman spaces Hankel operators Mean oscillation 

Mathematics Subject Classification

Primary 47B35 Secondary 32A37 

Notes

Acknowledgements

This work was done while the first author was visiting the Memorial University of Newfoundland in Canada. She wishes to thank Professor Jie Xiao and the Department of Mathematics and Statistics at MUN for hosting her visit. Finally, we wish to thank the referees for a very careful reading of the first draft of the paper and for making several thoughtful suggestions that helped us improve the presentation in this final version.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsHuzhou UniversityHuzhouChina
  2. 2.Department of Mathematics and StatisticsSUNY AlbanyAlbanyUSA
  3. 3.Department of MathematicsShantou UniversityShantouChina

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