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arXiv · 1406.4163

A sharp constant for the Bergman projection

Marijan Markovic
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Abstract

For the Bergman projection operator $P$ we prove that $ \|P\|_{{L^1(B,d\lambda)\rightarrow B_1}}= \frac {(2n+1)!}{n!}.$ Here $\lambda$ stands for the invariant metric in the unit ball $B$ of $\mathbf{C}^n$, 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 Per\"{a}l\"{a}.

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Marijan Markovic. 2014-06-16. A sharp constant for the Bergman projection. https://arxiv.org/abs/1406.4163

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