On weighted Bergman kernels of bounded domains

Sorin Dragomir

Studia Mathematica (1994)

  • Volume: 108, Issue: 2, page 149-157
  • ISSN: 0039-3223

Abstract

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We build on work by Z. Pasternak-Winiarski [PW2], and study a-Bergman kernels of bounded domains Ω ⊂ ℂ N for admissible weights a ∈ L ¹ ( Ω ) .

How to cite

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Dragomir, Sorin. "On weighted Bergman kernels of bounded domains." Studia Mathematica 108.2 (1994): 149-157. <http://eudml.org/doc/216046>.

@article{Dragomir1994,
abstract = {We build on work by Z. Pasternak-Winiarski [PW2], and study a-Bergman kernels of bounded domains $Ω ⊂ ℂ^N$ for admissible weights $a ∈ L¹(Ω)$.},
author = {Dragomir, Sorin},
journal = {Studia Mathematica},
keywords = {admissible weight; a-Bergman kernel; a-Bergman metric; weighted Bergman kernels; bounded domain; group of holomorphic diffeomorphisms},
language = {eng},
number = {2},
pages = {149-157},
title = {On weighted Bergman kernels of bounded domains},
url = {http://eudml.org/doc/216046},
volume = {108},
year = {1994},
}

TY - JOUR
AU - Dragomir, Sorin
TI - On weighted Bergman kernels of bounded domains
JO - Studia Mathematica
PY - 1994
VL - 108
IS - 2
SP - 149
EP - 157
AB - We build on work by Z. Pasternak-Winiarski [PW2], and study a-Bergman kernels of bounded domains $Ω ⊂ ℂ^N$ for admissible weights $a ∈ L¹(Ω)$.
LA - eng
KW - admissible weight; a-Bergman kernel; a-Bergman metric; weighted Bergman kernels; bounded domain; group of holomorphic diffeomorphisms
UR - http://eudml.org/doc/216046
ER -

References

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  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. Zbl0774.35048
  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. Zbl0158.11002
  5. [J] F. John, Partial Differential Equations, Springer, New York, 1982. Zbl0472.35001
  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. Zbl0422.53032
  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. Zbl0677.46015
  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. Zbl0223.32001
  13. [PW1] Z. Pasternak-Winiarski, On the dependence of the reproducing kernel on the weight of integration, J. Funct. Anal. 94 (1990), 110-134. Zbl0739.46010
  14. [PW2] Z. Pasternak-Winiarski, On weights which admit the reproducing kernel of Bergman type, Internat. J. Math. Math. Sci. 15 (1992), 1-14. Zbl0749.32019

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