On weighted Bergman kernels of bounded domains

• Autorzy: Sorin Dragomir
• Języki publikacji: EN

Abstrakty

EN

We build on work by Z. Pasternak-Winiarski [PW2], and study a-Bergman kernels of bounded domains $Ω ⊂ ℂ^N$ for admissible weights $a ∈ L¹(Ω)$.

Słowa kluczowe

EN

admissible weight; a-Bergman kernel; a-Bergman metric

Kategorie tematyczne

• 32Q15: K\"ahler manifolds
• 32A25: Integral representations; canonical kernels (Szeg\H o, Bergman, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 108
• Numer: 2
• Strony: 149-157

Daty

wydano

1994

otrzymano

1992-10-08

poprawiono

1998-07-04

Twórcy

autor

Sorin Dragomir

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

Bibliografia

• [Be] S. Bergman, Über die Kernfunktion eines Bereiches und ihr Verhalten am Rande, J. Reine Angew. Math. 169 (1933), 1-42.
• [Bo] B. Berndtsson, Weighted estimates for ∂̅ in domains in ℂ, preprint, Göteborg, 1992.
• [He] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978, 352-372.
• [Ho] L. Hörmander, L² estimates and existence theorems for the ∂̅ operator, Acta Math. 113 (1965), 89-152.
• [J] F. John, Partial Differential Equations, Springer, New York, 1982.
• [Ke] N. Kerzman, The Bergman kernel function. Differentiability at the boundary, Math. Ann. 195 (1972), 149-158.
• [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.
• [Ko] J. J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds I, II, Ann. of Math. 78 (1963), 112-148; 79 (1964), 450-472.
• [Ku] A. Kufner, Weighted Sobolev Spaces, Wiley, Chichester, 1985.
• [M1] T. Mazur, Canonical isometry on weighted Bergman spaces, Pacific J. Math. 136 (1989), 303-310.
• [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.
• [N] R. Narasimhan, Several Complex Variables, The Univ. of Chicago Press, Chicago, 1971.
• [PW1] Z. Pasternak-Winiarski, On the dependence of the reproducing kernel on the weight of integration, J. Funct. Anal. 94 (1990), 110-134.
• [PW2] Z. Pasternak-Winiarski, On weights which admit the reproducing kernel of Bergman type, Internat. J. Math. Math. Sci. 15 (1992), 1-14.