A note on Bloch functions

Authors

  • Cho-Ho CHU School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, U.K., e-mail: c.chu@qmul.ac.uk

DOI:

https://doi.org/10.24193/subbmath.2022.2.10

Keywords:

Bloch function, Bloch space, Bounded symmetric domain.

Abstract

We construct a natural linear isomorphism between the little Bloch space B₀ and the Banach space c₀ of complex null sequences. This paper is written for the special issue of Studia Universitatis Babe¸s-Bolyai Mathematica in memory of Professor Gabriela Kohr.

Mathematics Subject Classification (2010): 30H30, 32A18.

Received 5 August 2021; Accepted 27 August 2021.

References

Anderson, J.M., Clunie J., Pommerenke, Ch., On Bloch functions and normal functions, J. Reine Angew. Math. 270(1974), 12-37.

Chu, C.-H., Bounded Symmetric Domains in Banach Spaces, World Scientific, Singapore, 2020.

Chu, C.-H., Hamada, H., Honda, T., Kohr, G., Bloch functions on bounded symmetric domains, J. Funct. Anal., 272(2017), 2412-2441.

Chu, C.-H., Hamada, H., Honda, T., Kohr, G., Bloch space of a bounded symmetric domain and composition operators, Complex Anal. Oper. Theory, 13(2019), 479-492.

Dunford, N., Schwartz, J.T., Linear Operators, Wiley Classics Library Edition, New York, 1988.

Pelczynski, A., Projections in certain Banach spaces, 19(1960), 209-228.

Shields, A.L., Williams, D.L., Bounded projections, duality and multipliers in spaces of harmonic functions, J. Reine Angew. Math., 299(1978), 256-279.

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Published

2022-06-10

How to Cite

CHU, C.-H. (2022). A note on Bloch functions. Studia Universitatis Babeș-Bolyai Mathematica, 67(2), 345–350. https://doi.org/10.24193/subbmath.2022.2.10

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