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 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 
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     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 },
     year = {2015},
     volume = {_N_S_98},
     number = {112},
     doi = {10.2298/PIM150220023V},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM150220023V/}
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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

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