Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

UNBOUNDEDNESS OF THE BERGMAN PROJECTIONS ON $L^{p}$ SPACES WITH EXPONENTIAL WEIGHTS

Milutin R. Dostanića1

a1 Matematicki Fakultet, Studentski Trg 16, 11000 Beograd, Serbia and Montenegro (domi@matf.bg.ac.yu)

Abstract

We prove that the Bergman projection on $L^p(w)$ $(p\neq 2)$, where $w(r)=(1-r^2)^A\textrm{e}^{-B/(1-r^2)^{\alpha}}$, is not bounded.

AMS 2000 Mathematics subject classification: Primary 47B10

(Received February 12 2001)

Keywords

  • Bergman kernel;
  • Bergman projection;
  • Laplace method