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On boundary behaviour of the Bergman projection on pseudoconvex domains

100%

Jasiczak M.

Studia Mathematica

2005

tom 166

nr 3

243-261

It is shown that on strongly pseudoconvex domains the Bergman projection maps a space $Lv_{k}$ of functions growing near the boundary like some power of the Bergman distance from a fixed point into a space of functions which can be estimated by the consecutive power of the Bergman distance. This property has a local character. Let Ω be a bounded, pseudoconvex set with C³ boundary. We show that if the Bergman projection is continuous on a space $E ⊃ L^{∞}(Ω)$ defined by weighted-sup seminorms and equipped with the topology given by these seminorms, then E must contain the spaces $Lv_{k}$ for each natural k. As a result, in the case of strongly pseudoconvex domains the inductive limit of this sequence of spaces is the smallest extension of $L^{∞}$ in the class of spaces defined by weighted-sup seminorms on which the Bergman projection is continuous. This is a generalization of the results of J. Taskinen in the case of the unit disc as well as of the previous research of the author concerning the unit ball.

On locally convex extension of $H^{∞}$ in the unit ball and continuity of the Bergman projection

100%

Jasiczak M.

Studia Mathematica

2003

tom 156

nr 3

261-275

We define locally convex spaces LW and HW consisting of measurable and holomorphic functions in the unit ball, respectively, with the topology given by a family of weighted-sup seminorms. We prove that the Bergman projection is a continuous map from LW onto HW. These are the smallest spaces having this property. We investigate the topological and algebraic properties of HW.

Ograniczanie wyników

2 Studia Mathematica

2 Jasiczak M.

1 2005

1 2003

Wyniki wyszukiwania

On boundary behaviour of the Bergman projection on pseudoconvex domains

On locally convex extension of $H^{∞}$ in the unit ball and continuity of the Bergman projection