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

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home


Pick a mirror


On some class of integral operators related to the Bergman projection

Djordjije Vujadinovic

Faculty of Natural Sciences and Mathematics, University of Montenegro, Podgorica, Montenegro

Abstract: We consider the integral operator $$ C_\alpha f(z)=\int_D\frac{f(\xi)}{(1-z\bar{\xi})^{\alpha}} dA(\xi),\quad z\in D, $$ 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.

© 2015 Mathematical Institute of the Serbian Academy of Science and Arts
© 2015–2016 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition