Rhaly Operators on Small Weighted Hardy Spaces

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.

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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

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

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Correspondence to Le Hai Khoi.

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Lin, T.P., Doan, M.L. & Khoi, L.H. Rhaly Operators on Small Weighted Hardy Spaces. Acta Math Vietnam 43, 749–759 (2018). https://doi.org/10.1007/s40306-018-0277-9

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Keywords

  • Hilbert spaces
  • Entire functions
  • Rhaly operators

Mathematics Subject Classification (2010)

  • 30D15
  • 47B37