On the Cesàro operator in the Hardy space in the upper half plane

Authors

  • Valentin V. Andreev Department of Mathematics, Lamar University, Beaumont, ТХ, USA
  • Miron B. Bekker Department of Mathematics, University of Pittsburgh at Johnstown, Johnstown, PA, USA
  • Joseph A. Cima Department of Mathematics, University of North Carolina at Chapel Hill, Phillips Hall, Chapel Hill, NC, USA

DOI:

https://doi.org/10.3842/umzh.v77i6.8523

Keywords:

Cesàro operator, Hardy space, reproducing kernel, unitary operator.

Abstract

UDC 517.9

We consider the Cesàro operator in the Hardy space in the upper half plane. We provide a new simple proof of boundedness of this operator and show that this operator is equal to the sum of the identity operator and a unitary operator, which implies its normality.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 77, No. 6, 2025.

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Published

01.08.2025

Issue

Vol. 77 No. 6 (2025)

Section

Research articles

License

Copyright (c) 2025 Valentin V. Andreev, Miron B. Bekker, Joseph A. Cima

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Andreev, Valentin V., et al. “On the Cesàro Operator in the Hardy Space in the Upper Half Plane”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 6, Aug. 2025, pp. 441–442, https://doi.org/10.3842/umzh.v77i6.8523.