ArticleOriginal scientific text

Title

On weighted Bergman kernels of bounded domains

Authors 1

Affiliations

  1. Politecnico di Milano, Dipartimento di Matematica, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

Abstract

We build on work by Z. Pasternak-Winiarski [PW2], and study a-Bergman kernels of bounded domains ΩN for admissible weights aL¹(Ω).

Keywords

admissible weight, a-Bergman kernel, a-Bergman metric

Bibliography

  1. [Be] S. Bergman, Über die Kernfunktion eines Bereiches und ihr Verhalten am Rande, J. Reine Angew. Math. 169 (1933), 1-42.
  2. [Bo] B. Berndtsson, Weighted estimates for ∂̅ in domains in ℂ, preprint, Göteborg, 1992.
  3. [He] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978, 352-372.
  4. [Ho] L. Hörmander, L² estimates and existence theorems for the ∂̅ operator, Acta Math. 113 (1965), 89-152.
  5. [J] F. John, Partial Differential Equations, Springer, New York, 1982.
  6. [Ke] N. Kerzman, The Bergman kernel function. Differentiability at the boundary, Math. Ann. 195 (1972), 149-158.
  7. [Kl] P. F. Klembeck, Kähler metrics of negative curvature, the Bergman metric near the boundary, and the Kobayashi metric on smooth bounded strictly pseudoconvex sets, Indiana Univ. Math. J. (2) 27 (1978), 275-282.
  8. [Ko] J. J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds I, II, Ann. of Math. 78 (1963), 112-148; 79 (1964), 450-472.
  9. [Ku] A. Kufner, Weighted Sobolev Spaces, Wiley, Chichester, 1985.
  10. [M1] T. Mazur, Canonical isometry on weighted Bergman spaces, Pacific J. Math. 136 (1989), 303-310.
  11. [M2] T. Mazur, On the complex manifolds of Bergman type, in: Classical Analysis, Proc. 6-th Symposium, 23-29 September 1991, Poland, World Scientific, 1992, 132-138.
  12. [N] R. Narasimhan, Several Complex Variables, The Univ. of Chicago Press, Chicago, 1971.
  13. [PW1] Z. Pasternak-Winiarski, On the dependence of the reproducing kernel on the weight of integration, J. Funct. Anal. 94 (1990), 110-134.
  14. [PW2] Z. Pasternak-Winiarski, On weights which admit the reproducing kernel of Bergman type, Internat. J. Math. Math. Sci. 15 (1992), 1-14.
Pages:
149-157
Main language of publication
English
Received
1992-10-08
Accepted
1998-07-04
Published
1994
Exact and natural sciences