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Volterra Integral Operators from Campanato Spaces into General Function Spaces

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Abstract

In this paper, the boundedness and compactness of embedding from Campanato spaces \(\mathcal{L}_{p,\lambda}\) into tent spaces \(\mathcal{T}_{p,s}(\mu)\) are investigated. As an application, we give a characterization for the boundedness of the Volterra integral operator \(J_{g}\) from \(\mathcal{L}_{p,\lambda}\) to general function spaces \(F(p,p-1-\lambda,s)\). Meanwhile, the operator \(I_{g}\) and the multiplication operator \(M_{g}\) from \(\mathcal{L}_{p,\lambda}\) to \(F(p,p-1-\lambda,s)\) are studied. Furthermore, the essential norm of \(J_{g}\) and \(I_{g}\) from \(\mathcal{L}_{p,\lambda}\) to \(F(p,p-1-\lambda,s)\) is also considered.

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Funding

Xiangling Zhu is the corresponding author. The first author was supported by National Natural Science Foundation of China (projects nos. 11801250 and 11871257), Overseas Scholarship Program for Elite Young and Middle-Aged Teachers of Lingnan Normal University, the Key Program of Lingnan Normal University (project no. LZ1905), Yanling Youqing Program of Lingnan Normal University (project no. YL20200202), Department of Education of Guangdong Province (no. 2018KTSCX133), and the Innovation and Developing School Project of Guangdong Province (project no. 2019KZDXM032).

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Authors and Affiliations

  1. Lingnan Normal University, Guangdong, P. R. China

    R. Qian

  2. University of Electronic Science and Technology of China, Zhongshan, P. R. China

    X. Zhu

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  1. R. Qian
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  2. X. Zhu
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Correspondence to R. Qian or X. Zhu.

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Qian, R., Zhu, X. Volterra Integral Operators from Campanato Spaces into General Function Spaces. J. Contemp. Mathemat. Anal. 56, 158–167 (2021). https://doi.org/10.3103/S1068362321030067

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