Geodesic
On Some Class of Integral Operators Related to the Bergman Projection
Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 97

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We consider the integral operator $ C_lpha f(z)=ıt_D\frac{f(\xi)}{(1-z\bar{\xi})^{lpha}}\,dA(\xi),\quad zı D, $ where $0\alpha2$ and $D$ is the unit disc in the complex plane. and investigate boundedness of it on the space $L^p(D,d\lambda)$, $1$, 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.
DOI : 10.2298/PIM150220023V
Classification : 46E15, 46E20
Keywords: Bergman projection, singular numbers of a compact operator 
@article{10_2298_PIM150220023V,
     author = {Djordjije Vujadinovi\'c},
     title = {On {Some} {Class} of {Integral} {Operators} {Related} to the {Bergman} {Projection}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {97 },
     publisher = {mathdoc},
     volume = {_N_S_98},
     number = {112},
     year = {2015},
     doi = {10.2298/PIM150220023V},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM150220023V/}
}
TY  - JOUR
AU  - Djordjije Vujadinović
TI  - On Some Class of Integral Operators Related to the Bergman Projection
JO  - Publications de l'Institut Mathématique
PY  - 2015
SP  - 97 
VL  - _N_S_98
IS  - 112
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2298/PIM150220023V/
DO  - 10.2298/PIM150220023V
LA  - en
ID  - 10_2298_PIM150220023V
ER  - 
%0 Journal Article
%A Djordjije Vujadinović
%T On Some Class of Integral Operators Related to the Bergman Projection
%J Publications de l'Institut Mathématique
%D 2015
%P 97 
%V _N_S_98
%N 112
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2298/PIM150220023V/
%R 10.2298/PIM150220023V
%G en
%F 10_2298_PIM150220023V
Djordjije Vujadinović. On Some Class of Integral Operators Related to the Bergman Projection. Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 97 . doi: 10.2298/PIM150220023V

Cité par Sources :