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

• Autorzy: M. Jasiczak
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46A13: Spaces defined by inductive or projective limits (LB, LF, etc.)
• 32A36: Bergman spaces
• 32A70: Functional analysis techniques \SeeMainly{}
• 46E10: Topological linear spaces of continuous, differentiable or analytic functions
• 32A25: Integral representations; canonical kernels (Szeg\H o, Bergman, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 156
• Numer: 3
• Strony: 261-275

Daty

wydano

2003

Twórcy

autor

M. Jasiczak

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

Identyfikatory

DOI

10.4064/sm156-3-4