Abstract
On the basis of the characterizations of the boundedness and compactness of the Volterra type operator \(I_{g, \varphi }\) from mixed-norm spaces \(H(p,\, q,\, \phi )\) to Zygmund spaces \( \mathcal {Z}\), the authors provide a function-theoretic estimate for the essential norm of Volterra type operator \(I_{g, \varphi }\) by means of the definition of the essential norm of an operator and the properties of the analytic function. An estimate for the essential norm of the generalized integration operator
from Bloch-type spaces to F(p, q, s) spaces is also obtained.
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Acknowledgements
The authors are very grateful to anonymous referees and editors for their valuable and detailed suggestions and insightful comments to improve the original manuscript. The project is supported by the Natural Science Foundation of China (Grant nos. 11771184, 11771188) and the Foundation Research Project of Jiangsu Province of China (no. BK20161158).
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Communicated by Orr Moshe Shalit.
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Liu, X., Liu, Y., Xia, L. et al. The essential norm of the integral type operators. Banach J. Math. Anal. 14, 181–202 (2020). https://doi.org/10.1007/s43037-019-00028-y
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DOI: https://doi.org/10.1007/s43037-019-00028-y