1E.T.S. Arquitectura Departamento de Matemática Aplicada Universidad Politécnica de Valencia E-46071 Valencia, Spain 2MÚ AV ČR Žitná 25 11567 Praha 1, Czech Republic 3Department of Mathematics and Statistics University of Helsinki P.O. Box 68 FIN-00014 Helsinki, Finland
Studia Mathematica, Tome 171 (2005) no. 1, pp. 67-92
We consider Bergman projections and some new generalizations of
them on weighted $L^\infty ( {\mathbb D} )$-spaces. A new reproducing formula
is obtained. We show the boundedness of these projections for a
large family of weights $v$ which tend to 0 at the boundary with
a polynomial speed.
These weights may even be nonradial.
For logarithmically decreasing weights bounded projections do not
exist. In this case we instead consider
the projective description problem for
holomorphic inductive limits.
Keywords:
consider bergman projections generalizations weighted infty mathbb spaces reproducing formula obtained boundedness these projections large family weights which tend boundary polynomial speed these weights may even nonradial logarithmically decreasing weights bounded projections exist instead consider projective description problem holomorphic inductive limits
Affiliations des auteurs :
José Bonet
1
;
Miroslav Engliš
2
;
Jari Taskinen
3
1
E.T.S. Arquitectura Departamento de Matemática Aplicada Universidad Politécnica de Valencia E-46071 Valencia, Spain
2
MÚ AV ČR Žitná 25 11567 Praha 1, Czech Republic
3
Department of Mathematics and Statistics University of Helsinki P.O. Box 68 FIN-00014 Helsinki, Finland
@article{10_4064_sm171_1_4,
author = {Jos\'e Bonet and Miroslav Engli\v{s} and Jari Taskinen},
title = {Weighted $L^{\infty}$-estimates for {Bergman} projections},
journal = {Studia Mathematica},
pages = {67--92},
year = {2005},
volume = {171},
number = {1},
doi = {10.4064/sm171-1-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm171-1-4/}
}
TY - JOUR
AU - José Bonet
AU - Miroslav Engliš
AU - Jari Taskinen
TI - Weighted $L^{\infty}$-estimates for Bergman projections
JO - Studia Mathematica
PY - 2005
SP - 67
EP - 92
VL - 171
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/sm171-1-4/
DO - 10.4064/sm171-1-4
LA - en
ID - 10_4064_sm171_1_4
ER -
%0 Journal Article
%A José Bonet
%A Miroslav Engliš
%A Jari Taskinen
%T Weighted $L^{\infty}$-estimates for Bergman projections
%J Studia Mathematica
%D 2005
%P 67-92
%V 171
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/sm171-1-4/
%R 10.4064/sm171-1-4
%G en
%F 10_4064_sm171_1_4
José Bonet; Miroslav Engliš; Jari Taskinen. Weighted $L^{\infty}$-estimates for Bergman projections. Studia Mathematica, Tome 171 (2005) no. 1, pp. 67-92. doi: 10.4064/sm171-1-4
