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A Sharp Constant for the Bergman Projection

Published online by Cambridge University Press:  20 November 2018

Marijan Marković
Marijan Marković*
Affiliation:
Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put b.b., 81000 Podgorica, Montenegro. e-mail: marijanmmarkovic@gmail.com
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Abstract

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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.

Keywords

45P0547B35Bergman projectionsBesov spaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 1 , 01 March 2015 , pp. 128 - 133
Copyright
Copyright © Canadian Mathematical Society 2015

References

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