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A Sharp Constant for the Bergman Projection
Published online by Cambridge University Press: 20 November 2018
Abstract
For the Bergman projection operator $P$ we prove that
$$\left\| P:\,{{L}^{1}}\left( B,\,d\lambda \right)\,\to \,{{B}_{1}} \right\|\,=\,\frac{\left( 2n\,+\,1 \right)!}{n!}.$$
Here $\lambda$ stands for the hyperbolic metric in the unit ball
$B$ of
${{\mathbb{C}}^{n}}$, and
${{B}_{1}}$ denotes the Besov space with an adequate semi-norm. We also consider a generalization of this result. This generalizes some recent results due to Perälä.
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- Copyright © Canadian Mathematical Society 2015
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