Publications de l'Institut Mathématique, Nouvelle Série Vol. 98(112), pp. 97–107 (2015) 

On some class of integral operators related to the Bergman projectionDjordjije VujadinovicFaculty of Natural Sciences and Mathematics, University of Montenegro, Podgorica, MontenegroAbstract: We consider the integral operator $$ C_\alpha f(z)=\int_D\frac{f(\xi)}{(1z\bar{\xi})^{\alpha}} dA(\xi),\quad z\in D, $$ where $0<\alpha<2$ and $D$ is the unit disc in the complex plane. and investigate boundedness of it on the space $L^p(D,d\lambda)$, $1<p<\infty$, where $d\lambda$ is the Möbius invariant measure in $D$. We also consider the spectral properties of $C_\alpha$ when it acts on the Hilbert space $L^2(D,d\lambda)$, i.e., in the case $p=2$, when $C_\alpha$ maps $L^2(D,d\lambda)$ into the Dirichlet space. Keywords: Bergman projection; singular numbers of a compact operator Classification (MSC2000): 46E15; 46E20 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 18 Nov 2015. This page was last modified: 6 Jan 2016.
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