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Weighted composition operators on spaces generated by fractional Cauchy kernels of the unit ball

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Abstract

In this paper, we characterize bounded and compact weighted composition operators acting from spaces generated by fractional Cauchy kernels of the unit ball to Hardy spaces of the unit ball. We explicitly obtain the norm of such operators acting between these spaces and characterize the equicontinuity of a family of weighted composition operators acting between these spaces. Equivalent conditions characterizing compact weighted composition operators in terms of continuity of some integral transforms and equi-absolute continuity of special type of measures are also given.

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Acknowledgements

The authors are thankful to the referees for pointing out several errors. Their valuable comments and suggestions improved this paper significantly.

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Authors and Affiliations

  1. Department of Mathematics, Central University of Jammu, Raya-Suchani (Bagla), Samba, J&K, 181143, India

    Ajay K. Sharma

  2. Department of Mathematics, Baba Ghulam Shah Badshah University, Rajouri, J &K, 185234, India

    Javid Iqbal & Shayesta Farooq

  3. Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan

    M. Mursaleen

  4. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    M. Mursaleen

Authors
  1. Ajay K. Sharma
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  2. Javid Iqbal
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  3. Shayesta Farooq
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  4. M. Mursaleen
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The authors contributed equally and significantly in writing this paper.

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Correspondence to M. Mursaleen.

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Communicated by S Ponnusamy.

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Sharma, A.K., Iqbal, J., Farooq, S. et al. Weighted composition operators on spaces generated by fractional Cauchy kernels of the unit ball. J Anal 32, 1507–1517 (2024). https://doi.org/10.1007/s41478-023-00700-5

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  • DOI: https://doi.org/10.1007/s41478-023-00700-5

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