Reproducing properties and L p -estimates for Bergman projections in Siegel domains of type II

David Békollé; Anatole Temgoua Kagou

Studia Mathematica (1995)

  • Volume: 115, Issue: 3, page 219-239
  • ISSN: 0039-3223

Abstract

top
On homogeneous Siegel domains of type II, we prove that under certain conditions, the subspace of a weighted L p -space (0 < p < ∞) consisting of holomorphic functions is reproduced by a weighted Bergman kernel. We also obtain some L p -estimates for weighted Bergman projections. The proofs rely on a generalization of the Plancherel-Gindikin formula for the Bergman space A 2 .

How to cite

top

Békollé, David, and Temgoua Kagou, Anatole. "Reproducing properties and $L^p$-estimates for Bergman projections in Siegel domains of type II." Studia Mathematica 115.3 (1995): 219-239. <http://eudml.org/doc/216209>.

@article{Békollé1995,
abstract = {On homogeneous Siegel domains of type II, we prove that under certain conditions, the subspace of a weighted $L^p$-space (0 < p < ∞) consisting of holomorphic functions is reproduced by a weighted Bergman kernel. We also obtain some $L^p$-estimates for weighted Bergman projections. The proofs rely on a generalization of the Plancherel-Gindikin formula for the Bergman space $A^2$.},
author = {Békollé, David, Temgoua Kagou, Anatole},
journal = {Studia Mathematica},
keywords = {-mapping; weighted Bergman projections; Siegel domains of type II; Plancherel-Gindikin formula},
language = {eng},
number = {3},
pages = {219-239},
title = {Reproducing properties and $L^p$-estimates for Bergman projections in Siegel domains of type II},
url = {http://eudml.org/doc/216209},
volume = {115},
year = {1995},
}

TY - JOUR
AU - Békollé, David
AU - Temgoua Kagou, Anatole
TI - Reproducing properties and $L^p$-estimates for Bergman projections in Siegel domains of type II
JO - Studia Mathematica
PY - 1995
VL - 115
IS - 3
SP - 219
EP - 239
AB - On homogeneous Siegel domains of type II, we prove that under certain conditions, the subspace of a weighted $L^p$-space (0 < p < ∞) consisting of holomorphic functions is reproduced by a weighted Bergman kernel. We also obtain some $L^p$-estimates for weighted Bergman projections. The proofs rely on a generalization of the Plancherel-Gindikin formula for the Bergman space $A^2$.
LA - eng
KW - -mapping; weighted Bergman projections; Siegel domains of type II; Plancherel-Gindikin formula
UR - http://eudml.org/doc/216209
ER -

References

top
  1. [B] D. Békollé, Solutions avec estimations de l'équation des ondes, in: Sém. Analyse Harmonique 1983-1984, Publ. Math. Orsay, 1985, 113-125. Zbl0595.35019
  2. [BeBo] D. Békollé and A. Bonami, Estimates for the Bergman and Szegö projections in two symmetric domains of n , Colloq. Math. 68 (1995), 81-100. Zbl0863.47018
  3. [CR] R. R. Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in L p , Astérisque 77 (1980), 11-66. Zbl0472.46040
  4. [DK] M. M. Dzhrbashyan and A. O. Karapetyan, Integral representations in a generalized upper half-plane, Izv. Akad. Nauk Armenii Mat. 25 (6) (1990), 507-533. 
  5. [FRu] F. Forelli and W. Rudin, Projections on spaces of holomorphic functions on balls, Indiana Univ. Math. J. 24 (1974), 593-602. Zbl0297.47041
  6. [G] S. G. Gindikin, Analysis in homogeneous domains, Russian Math. Surveys 19 (4) (1964), 1-89, 379-388 and ibid. 28 (1973), 688. Zbl0144.08101
  7. [KoS] A. Korányi and E. M. Stein, H 2 spaces of generalized half-planes, Studia Math. 44 (1972), 379-388. Zbl0224.32004
  8. [P] J. Peetre, A reproducing kernel, Boll. Un. Mat. Ital. (6) 3-A (1984), 373-382. Zbl0589.32009
  9. [R] R. Rochberg, Interpolation in Bergman spaces, Michigan Math. J. 29 (1982), 229-236. Zbl0496.32010
  10. [T] A. Temgoua Kagou, Domaines de Siegel de type II: noyau de Bergman, Thèse de 3 e cycle, Université de Yaoundé I, 1993. Zbl0920.32002

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.