L p -Boundedness of Bergman projections in tube domains over homogeneous cones
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 2, p. 477-511

In this paper, we generalize to all tube domains over homogeneous cones L p -continuity properties of the Bergman projection.

Published online : 2018-08-07
Classification:  32A20,  32A10,  32A25,  32A36
@article{ASNSP_2011_5_10_2_477_0,
     author = {Nana, Cyrille and Trojan, Bartosz},
     title = {$L^p$-Boundedness of Bergman projections in tube domains over homogeneous cones},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 10},
     number = {2},
     year = {2011},
     pages = {477-511},
     zbl = {1232.32001},
     mrnumber = {2856156},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2011_5_10_2_477_0}
}
Nana, Cyrille; Trojan, Bartosz. $L^p$-Boundedness of Bergman projections in tube domains over homogeneous cones. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 2, pp. 477-511. http://www.numdam.org/item/ASNSP_2011_5_10_2_477_0/

[1] D. Békollé and A. Bonami, Estimates for the Bergman and Szegö projections in two symmetric domains of n , Colloq. Math. 68 (1995), 81–100. | MR 1311766 | Zbl 0863.47018

[2] D. Békollé, A. Bonami and G. Garrigós, Littlewood-Paley decomposition related to symmetric cones, IMHOTEP J. Afr. Math. Pures Appl. 3 (2000). | MR 1905056 | Zbl 1014.32014

[3] D. Békollé, A. Bonami, G. Garrigós, C. Nana, M. M. Peloso and F. Ricci, Lecture notes on Bergman projectors in tube domains over cones: an analytic and geometric viewpoint, IMHOTEP J. Afr. Math. Pures Appl. 5 (2004). | MR 2244169 | Zbl 1286.32001

[4] D. Békollé, A. Bonami, G. Garrigós and F. Ricci, Littlewood-Paley decomposition related to symmetric cones and Bergman projections in tube domains, Proc. London Math. Soc. (3) 89 (2004), 317–360. | MR 2078706 | Zbl 1079.42015

[5] D. Békollé, A. Bonami, M. M. Peloso and F. Ricci, Boundedness of weighted Bergman projections on tube domains over light cones, Math. Z. 237 (2001), 31–59. | MR 1836772 | Zbl 0983.32001

[6] D. Békollé and C. Nana, L p -boundedness of Bergman projections in the tube domain over Vinberg’s cone, J. Lie Theory 17 (2007), 115–144. | MR 2286885 | Zbl 1135.32004

[7] D. Békollé D. and A. Temgoua, Reproducing properties and L p -estimates for Bergman projections in Siegel domains of type II, Studia Math. 3 (1995), 219–239. | MR 1351238 | Zbl 0842.32016

[8] C. B. Chua, Relating Homogeneous cones and positive definite cones via T-algebras, SIAM J. Optim 14, 5400–506. | MR 2048159 | Zbl 1046.90058

[9] J. Dorfmeister and M. Koecher, Reguläre Kegel, Jahresber. Deutsch. Math.-Verein. 81 (1979), 109–151. | MR 544691 | Zbl 0418.17013

[10] D. Debertol, Besov spaces and the boundedness of weighted Bergman projections over symmetric tube domains, Publ. Math. 49 (2005), 21–72. | MR 2140199 | Zbl 1097.32002

[11] J. Faraut and A. Korányi, “Analysis on Symmetric Cones”, Clarendon Press, Oxford, 1994. | MR 1446489 | Zbl 0841.43002

[12] F. Forelli and W. Rudin, Projections on spaces of holomorphic functions in balls, Indiana Univ. Math. J. 24 (1974), 593–602. | MR 357866 | Zbl 0297.47041

[13] S. G. Gindikin, Analysis on homogeneous domains, Russian Math. Surveys 19 (1964), 1–83. | MR 171941 | Zbl 0144.08101

[14] G. Garrigós and A. Seeger, Plate decompositions for cone multipliers, In: “Harmonic Analysis and its Applications at Sapporo 2005”, Miyachi & Tachizawa Ed. Hokkaido University Report Series, Vol. 103, 13–28. | Zbl 1196.42010

[15] H. Ishi, Basic relative invariants associated to homogeneous cones and applications, J. Lie Theory 11 (2001), 155–171. | MR 1828288 | Zbl 0976.43005

[16] H. Ishi, The gradient maps associated to certain non-homogeneous cones, Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), 44–46. | MR 2128930 | Zbl 1086.52501

[17] M. Spivak, “Differential Geometry”, Vol. I, Publish or Perish, Inc., 1970.

[18] A. Temgoua Kagou, “Domaines de Siegel de type II-Noyau de Bergman”, Thèse de 3e Cycle, Université de Yaoundé I, 1993.

[19] B. Trojan, Asymptotic expansions and Hua-harmonic functions on bounded homogeneous domains, Math. Ann. 336 (2006), 73–110. | MR 2242620 | Zbl 1108.32011

[20] E. B. Vinberg, The theory of convex homogeneous cones, Trudy Moskov Mat. Obšč. 12 (1963), 359–388. | MR 158414 | Zbl 0137.05603

[21] J. Young Ho, Jordan algebras associated to T-algebras, Bull. Korean Math. Soc. 32 (1995), 179–189. | MR 1356070 | Zbl 0849.17033