Abstract
Let \(\mathbb{B}\) be the unit ball of a complex Banach space X. In this paper, we generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball \(\mathbb{B}\) by using the radial derivative. Next, we define an extended Cesàro operator Tφ with holomorphic symbol φ and characterize those φ for which Tφ is bounded between the Bloch-type spaces and the little Bloch-type spaces. We also characterize those φ for which Tφ is compact between the Bloch-type spaces and the little Bloch-type spaces under some additional assumption on the symbol φ. When \(\mathbb{B}\) is the open unit ball of a finite dimensional complex Banach space X, this additional assumption is automatically satisfied.
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Acknowledgements
This work was supported by Japan Society for the Promotion of Science KAKENHI (Grant No. JP16K05217).
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Hamada, H. Bloch-type spaces and extended Cesàro operators in the unit ball of a complex Banach space. Sci. China Math. 62, 617–628 (2019). https://doi.org/10.1007/s11425-017-9183-5
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DOI: https://doi.org/10.1007/s11425-017-9183-5