On boundary behaviour of the Bergman projection on pseudoconvex domains

• Autorzy: M. Jasiczak
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 32A40: Boundary behavior of holomorphic functions
• 32F45: Invariant metrics and pseudodistances
• 32A36: Bergman spaces
• 32A70: Functional analysis techniques \SeeMainly{}
• 32T40: Peak functions
• 32A25: Integral representations; canonical kernels (Szeg\H o, Bergman, etc.)
• 32T15: Strongly pseudoconvex domains

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 166
• Numer: 3
• Strony: 243-261

Daty

wydano

2005

Twórcy

autor

M. Jasiczak

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

Identyfikatory

DOI

10.4064/sm166-3-3