Abstract
In this chapter, we study the Berezin transform on F α 2 and certain spaces of functions of bounded mean oscillation (BMO) on the complex plane. We first consider the Berezin symbol of a bounded linear operator on F α 2 and show that this is a Lipschitz function in the Euclidean metric. We then consider the Berezin transform of a function and show that there is a semigroup property with respect to the parameter α. We also consider the action of the Berezin transform on L p spaces and the behavior of the Berezin transform when it is iterated.
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Zhu, K. (2012). The Berezin Transform and BMO. In: Analysis on Fock Spaces. Graduate Texts in Mathematics, vol 263. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-8801-0_3
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DOI: https://doi.org/10.1007/978-1-4419-8801-0_3
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