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Difference of Weighted Composition Operators Over the Ball

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Abstract

Recently, Choe et al. obtained characterizations for bounded/compact differences of weighted composition operators acting from a standard weighted Bergman space into another over the unit disk. In this paper we extend those results to the ball setting. By devising a new approach regarding test functions, we improve the characterizations as well as the proofs. Namely, the Reproducing Kernel Thesis is added to the characterizations and our proofs, when restricted to the disk, are new and simpler.

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Acknowledgements

In the earlier version of the paper, the \(L^{q}_{\beta }\)-integrability condition for the weight functions was included (as in [1, 2]) as a standing hypothesis in our main theorems. We thank the referee for pointing out that such integrability condition can be removed as in the current paper. We hope that removing such integrability condition would significantly increase the utility of our characterizations in the study of various problems involving weighted composition operators.

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Authors and Affiliations

  1. Department of Mathematics, Korea University, Seoul, 02841, Korea

    Boo Rim Choe & Hyungwoon Koo

  2. Institute of Mathematical Sciences, Ewha Womans University, Seoul, 03760, Korea

    Koeun Choi & Inyoung Park

Authors
  1. Boo Rim Choe
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  2. Koeun Choi
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  3. Hyungwoon Koo
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  4. Inyoung Park
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Contributions

K. Choi, B. Choe, H. Koo and I. Park wrote the main manuscript text. All authors reviewed the manuscript.

Corresponding author

Correspondence to Koeun Choi.

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The authors declare no competing interests.

Additional information

Communicated by H. Turgay Kaptanoglu.

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B. Choe was supported by NRF (2023R1A2C1002489) of Korea, H. Koo was supported by NRF (2022R1F1A1063305) of Korea, I. Park was supported by NRF (2019R1A6A1A11051177) and NRF (2021R1I1A1A01047051) of Korea, and K. Choi was supported by NRF (2019R1A6A1A11051177) of Korea.

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Choe, B.R., Choi, K., Koo, H. et al. Difference of Weighted Composition Operators Over the Ball. Complex Anal. Oper. Theory 18, 33 (2024). https://doi.org/10.1007/s11785-023-01477-y

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  • DOI: https://doi.org/10.1007/s11785-023-01477-y

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