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A Sharp Constant for the Bergman Projection

  • Marijan Marković,
    Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put b.b., 81000 Podgorica, Montenegro
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Abstract

For the Bergman projection operator $P$ we prove that \begin{equation*} \|P\colon L^1(B,d\lambda)\rightarrow B_1\| = \frac {(2n+1)!}{n!}. \end{equation*} 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: Bergman projections, Besov spaces Bergman projections, Besov spaces
MSC Classifications: 45P05, 47B35 show english descriptions Integral operators [See also 47B38, 47G10]
Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
45P05 - Integral operators [See also 47B38, 47G10]
47B35 - Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
 

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