On weighted Bergman kernels of bounded domains
Dragomir, Sorin
Studia Mathematica, Tome 108 (1994), p. 149-157 / Harvested from The Polish Digital Mathematics Library

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

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:216046
@article{bwmeta1.element.bwnjournal-article-smv108i2p149bwm,
     author = {Sorin Dragomir},
     title = {On weighted Bergman kernels of bounded domains},
     journal = {Studia Mathematica},
     volume = {108},
     year = {1994},
     pages = {149-157},
     zbl = {0818.32006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv108i2p149bwm}
}
Dragomir, Sorin. On weighted Bergman kernels of bounded domains. Studia Mathematica, Tome 108 (1994) pp. 149-157. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv108i2p149bwm/

[00000] [Be] S. Bergman, Über die Kernfunktion eines Bereiches und ihr Verhalten am Rande, J. Reine Angew. Math. 169 (1933), 1-42.

[00001] [Bo] B. Berndtsson, Weighted estimates for ∂̅ in domains in ℂ, preprint, Göteborg, 1992. | Zbl 0774.35048

[00002] [He] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978, 352-372.

[00003] [Ho] L. Hörmander, L² estimates and existence theorems for the ∂̅ operator, Acta Math. 113 (1965), 89-152. | Zbl 0158.11002

[00004] [J] F. John, Partial Differential Equations, Springer, New York, 1982. | Zbl 0472.35001

[00005] [Ke] N. Kerzman, The Bergman kernel function. Differentiability at the boundary, Math. Ann. 195 (1972), 149-158.

[00006] [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. | Zbl 0422.53032

[00007] [Ko] J. J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds I, II, Ann. of Math. 78 (1963), 112-148; 79 (1964), 450-472.

[00008] [Ku] A. Kufner, Weighted Sobolev Spaces, Wiley, Chichester, 1985.

[00009] [M1] T. Mazur, Canonical isometry on weighted Bergman spaces, Pacific J. Math. 136 (1989), 303-310. | Zbl 0677.46015

[00010] [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.

[00011] [N] R. Narasimhan, Several Complex Variables, The Univ. of Chicago Press, Chicago, 1971. | Zbl 0223.32001

[00012] [PW1] Z. Pasternak-Winiarski, On the dependence of the reproducing kernel on the weight of integration, J. Funct. Anal. 94 (1990), 110-134. | Zbl 0739.46010

[00013] [PW2] Z. Pasternak-Winiarski, On weights which admit the reproducing kernel of Bergman type, Internat. J. Math. Math. Sci. 15 (1992), 1-14. | Zbl 0749.32019