Geodesic
Weighted $L^{\infty}$-estimates for Bergman projections
José Bonet1 ; Miroslav Engliš2 ; Jari Taskinen3
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
Studia Mathematica, Tome 171 (2005) no. 1, pp. 67-92 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm171-1-4
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

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 
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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

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