Abstract
The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Peláez, who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces. However, their characterizations for the boundedness are not complete. In this paper, the author completely characterizes the boundedness and compactness of Volterra type operators from the weighted Dirichlet spaces D pα to D qβ (−1 < α, β and 0 < p < q < ∞), which essentially complete their works. Furthermore, the author investigates the order boundedness of Volterra type operators between weighted Dirichlet spaces.
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Acknowledgements
The author is grateful to the referee for his (or her) valuable comments and suggestions. Also, he would like to thank the brilliant mathematician, Loo-Keng Hua, for his excellent books which had inspired him into mathematics. At last, he wants to express his gratitude to the great star, Bruce Lee, for inspiring him with the fighting spirit.
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This work was supported by the National Natural Science Foundation of China (No. 11801094).
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Lin, Q. Volterra Type Operators on Weighted Dirichlet Spaces. Chin. Ann. Math. Ser. B 42, 601–612 (2021). https://doi.org/10.1007/s11401-021-0281-6
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DOI: https://doi.org/10.1007/s11401-021-0281-6