Abstract
Let n > 1 and B be the unit ball in n dimensions complex space Cn. Suppose that φ is a holomorphic self-map of B and ψ ∈ H(B) with ψ(0) = 0. A kind of integral operator, composition Cesàro operator, is defined by
In this paper, the authors characterize the conditions that the composition Cesàro operator Tφ,ψ is bounded or compact on the normal weight Zygmund space \({{\cal Z}_\mu }\left( B \right)\). At the same time, the sufficient and necessary conditions for all cases are given.
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The authors thank the referees for their useful suggestions!
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This work was supported by the National Natural Science Foundation of China (No. 11571104) and the Hunan Provincial Innovation Foundation for Postgraduate (No. CX2018B286).
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Xu, S., Zhang, X. & Li, S. Composition Cesàro Operator on the Normal Weight Zygmund Space in High Dimensions. Chin. Ann. Math. Ser. B 42, 69–84 (2021). https://doi.org/10.1007/s11401-021-0245-x
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DOI: https://doi.org/10.1007/s11401-021-0245-x