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Acta Mathematica Vietnamica

, Volume 43, Issue 4, pp 749–759 | Cite as

Rhaly Operators on Small Weighted Hardy Spaces

  • Tan Pin Lin
  • Minh Luan Doan
  • Le Hai Khoi
Article

Abstract

We study several properties of Rhaly operators on small weighted Hardy spaces of holomorphic functions in the unit disc \(\mathbb {D}\). In particular, we obtain criteria for boundedness, compactness, Hilbert-Schmidt norm, and p-Schatten class membership of such operators. A closedness of Rhaly operator is also studied.

Keywords

Hilbert spaces Entire functions Rhaly operators 

Mathematics Subject Classification (2010)

30D15 47B37 

Notes

Acknowledgements

The authors would like to thank the referee for useful remarks. Thanks also go to Hervé Queffélec for valuable comments on the first draft of this paper.

Funding Information

Supported in part by MOE’s AcRF Tier 1 grants M4011166.110 (RG24/13) and M4011724.110 (RG128/16).

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological University (NTU)SingaporeSingapore
  2. 2.Department of MathematicsUniversity of Notre DameNotre DameUSA

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