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Weak Factorization and Hankel Forms for Bergman–Orlicz Spaces on the Unit Ball

  • Edgar TchoundjaEmail author
  • Ruhan Zhao
Article
  • 31 Downloads

Abstract

Let \({\mathbb {B}}^n\) be the unit ball of \({\mathbb {C}}^n\) and \({\mathcal {A}}^\Phi _\alpha ({\mathbb {B}}^n)\) be the Bergman–Orlicz space, consisting of holomorphic functions in \(L^\Phi _\alpha ({\mathbb {B}}^n)\). We characterize bounded Hankel operators between some Bergman–Orlicz spaces \({\mathcal {A}}^{\Phi _1}_\alpha ({\mathbb {B}}^n)\) and \(\mathcal A^{\Phi _2}_\alpha ({\mathbb {B}}^n)\) where \(\Phi _1\) and \(\Phi _2\) are convex growth functions. We then obtain weak factorization theorems for \({\mathcal {A}}^\Phi _\alpha ({\mathbb {B}}^n)\), with \(\Phi \) a convex growth function, into two Bergman–Orlicz spaces, generalizing the main result obtained in Pau and Zhao (Math Ann 363:363–383, 2015).

Keywords

Hankel operator Bergman–Orlicz spaces Weak factorization 

Mathematics Subject Classification

47B35 32A35 32A36 

Notes

Acknowledgements

The authors would like to thank the anonymous referee for his helpful comments.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUniversity of Yaoundé IYaoundéCameroon
  2. 2.Department of MathematicsSUNY BrockportBrockportUSA
  3. 3.Department of MathematicsShantou UniversityShantouChina

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