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Some properties of the integration operators on the spaces F(p, q, s)

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We study the closed range property and the strict singularity of integration operators acting on the spaces F(p, pα − 2, s). We completely characterize the closed range property of the Volterra companion operator Ig on F(p, pα − 2, s), which generalizes the existing results and answers a question raised in [A. Anderson, Integral Equations Operator Theory, 69 (2011), no. 1, 87–99]. For the Volterra operator Jg, we show that, for 0 < α ≤ 1, Jg never has a closed range on F (p, pα − 2, s). We then prove that the notions of compactness, weak compactness and strict singularity coincide in the case of Jg acting on F(p,p − 2, s).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710119, China

    Jiale Chen

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  1. Jiale Chen
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Correspondence to Jiale Chen.

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Conflict of Interest The author declares no conflict of interest.

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This work was partially supported by the Fundamental Research Funds for the Central Universities (GK202207018) of China.

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Chen, J. Some properties of the integration operators on the spaces F(p, q, s). Acta Math Sci 44, 173–188 (2024). https://doi.org/10.1007/s10473-024-0109-z

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  • DOI: https://doi.org/10.1007/s10473-024-0109-z

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