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On Quasi-Grand Lebesgue Spaces and the Hausdorff Operator

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Abstract

It is proved that the quasi-grand Lebesgue space \(G\psi _{a,b}\) is not normable. Also, the boundedness of the Hausdorff operator \(\displaystyle H_\varphi (f)(x):= \int _0^\infty \frac{\varphi (y)}{y}f\left( \frac{x}{y}\right) \textrm{d}y\) in the space \(G\psi _{a,b}\) has been investigated for a special case of the function \(\psi _{a,b}\).

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Acknowledgements

The first author acknowledges the MATRICS Research Grant No. MTR/2019/000783 of SERB, Department of Science and Technology, India. The third author acknowledges the JRF Research Grant No. 09/045(1716)/2019-EMR-I of CSIR, India.

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Authors and Affiliations

  1. Department of Mathematics, Dyal Singh College, University of Delhi, Lodhi Road, Delhi, 110 003, India

    Arun Pal Singh

  2. Department of Mathematics, South Asian University, Rajpur Road, Maidan Garhi, New Delhi, 110 068, India

    Pankaj Jain

  3. Department of Mathematics, University of Delhi, Delhi, 110 007, India

    Rahul Panchal

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  1. Arun Pal Singh
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  2. Pankaj Jain
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Correspondence to Pankaj Jain.

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Singh, A.P., Jain, P. & Panchal, R. On Quasi-Grand Lebesgue Spaces and the Hausdorff Operator. Bull. Malays. Math. Sci. Soc. 47, 14 (2024). https://doi.org/10.1007/s40840-023-01618-8

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  • DOI: https://doi.org/10.1007/s40840-023-01618-8

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