Abstract
In this chapter, we mainly study the \(\alpha \)-Bloch spaces, some operators acting on them, and their dual. We also introduce the space \(H^\infty _\alpha \). These spaces play a decisive role in studying the weighted composition operators on \(\mathcal {N}_p\)-spaces.
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References
Anderson, J.M.: Bloch functions: the basic theory. In: Operators and Function Theory (Lancaster, 1984). NATO Advanced Science Institutes Series C Mathematical and Physical Sciences, vol. 153, pp. 1–17. Reidel, Dordrecht (1985)
Anderson, J.M., Clunie, J., Pommerenke, C.: On Bloch functions and normal functions. J. Reine Angew. Math. 270, 12–37 (1974)
Lindström, M., Makhmutov, S., Taskinen, J.: The essential norm of a Bloch-to-\(Q_p\) composition operator. Can. Math. Bull. 47(1), 49–59 (2004)
Shields, A.L., Williams, D.L.: Bounded projections, duality, and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162, 287–302 (1971)
Ueki, S.-I.: Weighted composition operators acting between the \(\mathcal {N}_p\)-space and the weighted-type space \(H^\infty _\alpha \). Indag. Math. (N.S.) 23(3), 243–255 (2012)
Zhu, K.H.: Bloch type spaces of analytic functions. Rocky Mountain J. Math. 23(3), 1143–1177 (1993)
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Hai Khoi, L., Mashreghi, J. (2023). The \(\alpha \)-Bloch Spaces. In: Theory of Np Spaces. Frontiers in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-39704-2_4
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DOI: https://doi.org/10.1007/978-3-031-39704-2_4
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