Geodesic
On Grand and Small Bergman Spaces
Matematičeskie zametki, Tome 104 (2018) no. 3, pp. 439-446

Voir la notice de l'article provenant de la source Math-Net.Ru

Grand and small Bergman spaces of functions holomorphic in the unit disc are introduced. The boundedness of the Bergman projection operator on grand Bergman spaces is proved. The main result consists of estimates for functions in grand and small Bergman spaces near the boundary, which differ from those in the case of the classical Bergman space by a logarithmic multiplier with positive (for grand spaces) or negative (for small spaces) exponent.
Keywords: Bergman space, Bergman projection, grand Bergman space, small Bergman space, boundary estimates.
Mots-clés : grand Lebesgue space, small Lebesgue space 
@article{MZM_2018_104_3_a8,
     author = {A. N. Karapetyants and S. G. Samko},
     title = {On {Grand} and {Small} {Bergman} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {439--446},
     publisher = {mathdoc},
     volume = {104},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_3_a8/}
}
TY  - JOUR
AU  - A. N. Karapetyants
AU  - S. G. Samko
TI  - On Grand and Small Bergman Spaces
JO  - Matematičeskie zametki
PY  - 2018
SP  - 439
EP  - 446
VL  - 104
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_104_3_a8/
LA  - ru
ID  - MZM_2018_104_3_a8
ER  - 
%0 Journal Article
%A A. N. Karapetyants
%A S. G. Samko
%T On Grand and Small Bergman Spaces
%J Matematičeskie zametki
%D 2018
%P 439-446
%V 104
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_104_3_a8/
%G ru
%F MZM_2018_104_3_a8
A. N. Karapetyants; S. G. Samko. On Grand and Small Bergman Spaces. Matematičeskie zametki, Tome 104 (2018) no. 3, pp. 439-446. http://geodesic.mathdoc.fr/item/MZM_2018_104_3_a8/