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On boundary behaviour of the Bergman projection on pseudoconvex domains

M. Jasiczak (2005)

Studia Mathematica

It is shown that on strongly pseudoconvex domains the Bergman projection maps a space L v 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...

On exact sequences of quojections.

G. Metafune, V. B. Moscatelli (1991)

Revista Matemática de la Universidad Complutense de Madrid

We give some general exact sequences for quojections from which many interesting representation results for standard twisted quojections can be deduced. Then the methods are also generalized to the case of nuclear Fréchet spaces.

On locally convex extension of H in the unit ball and continuity of the Bergman projection

M. Jasiczak (2003)

Studia Mathematica

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.

On prequojections and their duals.

M. I. Ostrovskii (1998)

Revista Matemática Complutense

The paper is devoted to the class of Fréchet spaces which are called prequojections. This class appeared in a natural way in the structure theory of Fréchet spaces. The structure of prequojections was studied by G. Metafune and V. B. Moscatelli, who also gave a survey of the subject. Answering a question of these authors we show that their result on duals of prequojections cannot be generalized from the separable case to the case of spaces of arbitrary cardinality. We also introduce a special class...

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