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We consider Bergman projections and some new generalizations of them on weighted -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.
José Bonet, Miroslav Engliš, and Jari Taskinen. "Weighted $L^{∞}$-estimates for Bergman projections." Studia Mathematica 171.1 (2005): 67-92. <http://eudml.org/doc/284479>.
@article{JoséBonet2005, abstract = {We consider Bergman projections and some new generalizations of them on weighted $L^\{∞\}()$-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.}, author = {José Bonet, Miroslav Engliš, Jari Taskinen}, journal = {Studia Mathematica}, keywords = {Bergman projection; weighted estimate; projective description problem; holomorphic inductive limit}, language = {eng}, number = {1}, pages = {67-92}, title = {Weighted $L^\{∞\}$-estimates for Bergman projections}, url = {http://eudml.org/doc/284479}, volume = {171}, year = {2005}, }
TY - JOUR AU - José Bonet AU - Miroslav Engliš AU - Jari Taskinen TI - Weighted $L^{∞}$-estimates for Bergman projections JO - Studia Mathematica PY - 2005 VL - 171 IS - 1 SP - 67 EP - 92 AB - We consider Bergman projections and some new generalizations of them on weighted $L^{∞}()$-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. LA - eng KW - Bergman projection; weighted estimate; projective description problem; holomorphic inductive limit UR - http://eudml.org/doc/284479 ER -