Estimates for the Bergman and Szegö projections in two symmetric domains of n

David Bekollé; Aline Bonami

Colloquium Mathematicae (1995)

  • Volume: 68, Issue: 1, page 81-100
  • ISSN: 0010-1354

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Bekollé, David, and Bonami, Aline. "Estimates for the Bergman and Szegö projections in two symmetric domains of $ℂ^{n}$." Colloquium Mathematicae 68.1 (1995): 81-100. <http://eudml.org/doc/210298>.

@article{Bekollé1995,
author = {Bekollé, David, Bonami, Aline},
journal = {Colloquium Mathematicae},
keywords = {Bergman kernel; Szegö kernel; Hardy space; bounded symmetric domain; Lie ball; Bergman space; Bergman orthogonal projector; integral operator; Bloch space; holomorphically equivalent; transfer principle; Szegö orthogonal projector; Shilov boundary; stability group},
language = {eng},
number = {1},
pages = {81-100},
title = {Estimates for the Bergman and Szegö projections in two symmetric domains of $ℂ^\{n\}$},
url = {http://eudml.org/doc/210298},
volume = {68},
year = {1995},
}

TY - JOUR
AU - Bekollé, David
AU - Bonami, Aline
TI - Estimates for the Bergman and Szegö projections in two symmetric domains of $ℂ^{n}$
JO - Colloquium Mathematicae
PY - 1995
VL - 68
IS - 1
SP - 81
EP - 100
LA - eng
KW - Bergman kernel; Szegö kernel; Hardy space; bounded symmetric domain; Lie ball; Bergman space; Bergman orthogonal projector; integral operator; Bloch space; holomorphically equivalent; transfer principle; Szegö orthogonal projector; Shilov boundary; stability group
UR - http://eudml.org/doc/210298
ER -

References

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  1. [1] D. Bekollé, Solutions avec estimations de l'équation des ondes, in: Séminaire Analyse Harmonique 1983-1984, Publ. Math. Orsay, 1985, 113-125. Zbl0595.35019
  2. [2] D. Bekollé, Le dual de l'espace des fonctions holomorphes intégrables dans des domaines de Siegel, Ann. Inst. Fourier (Grenoble) 33 (3) (1984), 125-154. Zbl0513.32032
  3. [3] D. Bekollé et M. Omporo, Le dual de la classe de Bergman A 1 dans la boule de Lie de n , C. R. Acad. Sci. Paris 311 (1990), 235-238. 
  4. [4] D. Bekollé and A. Temgoua Kagou, Reproducing properties and L p estimates for Bergman projections in Siegel domains of type II, submitted. Zbl0842.32016
  5. [5] E. Cartan, Sur les domaines bornés homogènes de l'espace de n variables complexes, Abh. Math. Sem. Hamburg 11 (1935), 116-162. Zbl0011.12302
  6. [6] C. Fefferman, The multiplier problem for the ball, Ann. of Math. 94 (1971), 330-336. Zbl0234.42009
  7. [7] F. Forelli and W. Rudin, Projections on spaces of holomorphic functions in balls, Indiana Univ. Math. J. 24 (1974), 593-602. Zbl0297.47041
  8. [8] S. G. Gindikin, Analysis on homogeneous domains, Russian Math. Surveys 19 (1964), 1-89. 
  9. [9] L. K. Hua, Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, Transl. Math. Monographs 6, Amer. Math. Soc., Providence, 1963. 
  10. [10] B. Jöricke, Continuity of the Cauchy projection in Hölder norms for classical domains, Math. Nachr. 113 (1983), 227-244. Zbl0579.32006
  11. [11] A. Korányi and S. Vági, Singular integrals on homogeneous spaces and some problems of classical analysis, Ann. Scuola Norm. Sup. Pisa 25 (1971), 575-648. Zbl0291.43014
  12. [12] E. M. Stein, Some problems in harmonic analysis suggested by symmetric spaces and semi-simple groups, in: Proc. Intern. Congress of Math. Nice 1, 1970, 173-189. 
  13. [13] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, 1971. Zbl0232.42007
  14. [14] S. Vági, Harmonic analysis in Cartan and Siegel domains, in: Studies in Harmonic Analysis, J. M. Ash (ed.), MAA Stud. Math. 13, 1976, 257-309. Zbl0352.32031
  15. [15] S. Yan, Duality and differential operators on the Bergman spaces of bounded symmetric domains, J. Funct. Anal. 105 (1992), 171-187. Zbl0782.47028
  16. [16] K. H. Zhu, Duality and Hankel operators on the Bergman spaces of bounded symmetric domains, ibid. 81 (1988), 260-278. Zbl0669.47019

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