# 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

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topBékollé, 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- [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
- [BeBo] D. Békollé and A. Bonami, Estimates for the Bergman and Szegö projections in two symmetric domains of ${\u2102}^{n}$, Colloq. Math. 68 (1995), 81-100. Zbl0863.47018
- [CR] R. R. Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in ${L}^{p}$, Astérisque 77 (1980), 11-66. Zbl0472.46040
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- [FRu] F. Forelli and W. Rudin, Projections on spaces of holomorphic functions on balls, Indiana Univ. Math. J. 24 (1974), 593-602. Zbl0297.47041
- [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
- [KoS] A. Korányi and E. M. Stein, ${H}^{2}$ spaces of generalized half-planes, Studia Math. 44 (1972), 379-388. Zbl0224.32004
- [P] J. Peetre, A reproducing kernel, Boll. Un. Mat. Ital. (6) 3-A (1984), 373-382. Zbl0589.32009
- [R] R. Rochberg, Interpolation in Bergman spaces, Michigan Math. J. 29 (1982), 229-236. Zbl0496.32010
- [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

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