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The Berezin Transform and BMO

2012
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
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