Toeplitz and Hankel operators from Bergman to analytic Besov spaces of tube domains over symmetric cones
HTML articles powered by AMS MathViewer
- by C. Nana and B. F. Sehba
- St. Petersburg Math. J. 30 (2019), 723-750
- DOI: https://doi.org/10.1090/spmj/1567
- Published electronically: June 4, 2019
- PDF | Request permission
Abstract:
The bounded Toeplitz and Hankel operators from weighted Bergman spaces to weighted Besov spaces in tube domains over symmetric cones are characterized. Weak factorization results are deduced for some Bergman spaces in these settings.References
- David Békollé, The dual of the Bergman space $A^1$ in symmetric Siegel domains of type $\textrm {II}$, Trans. Amer. Math. Soc. 296 (1986), no. 2, 607–619. MR 846599, DOI 10.1090/S0002-9947-1986-0846599-X
- David Békollé and Aline Bonami, Estimates for the Bergman and Szegő projections in two symmetric domains of $\textbf {C}^n$, Colloq. Math. 68 (1995), no. 1, 81–100. MR 1311766, DOI 10.4064/cm-68-1-81-100
- David Békollé and Aline Bonami, Analysis on tube domains over light cones: some extensions of recent results, Actes des Rencontres d’Analyse Complexe (Poitiers-Futuroscope, 1999) Atlantique, Poitiers, 2002, pp. 17–37. MR 1944193
- David Békollé, Aline Bonami, and Gustavo Garrigós, Littlewood-Paley decompositions related to symmetric cones, IMHOTEP J. Afr. Math. Pures Appl. 3 (2000), no. 1, 11–41. MR 1905056
- David Békollé, Aline Bonami, Gustavo Garrigós, Cyrille Nana, Marco M. Peloso, and Fulvio Ricci, Lecture notes on Bergman projectors in tube domains over cones: an analytic and geometric viewpoint, IMHOTEP J. Afr. Math. Pures Appl. 5 (2004), Exp. I, front matter + ii + 75. MR 2244169
- D. Békollé, A. Bonami, G. Garrigós, and F. Ricci, Littlewood-Paley decompositions related to symmetric cones and Bergman projections in tube domains, Proc. London Math. Soc. (3) 89 (2004), no. 2, 317–360. MR 2078706, DOI 10.1112/S0024611504014765
- D. Békollé, A. Bonami, G. Garrigós, F. Ricci, and B. Sehba, Analytic Besov spaces and Hardy-type inequalities in tube domains over symmetric cones, J. Reine Angew. Math. 647 (2010), 25–56. MR 2729357, DOI 10.1515/CRELLE.2010.072
- David Bekollé, Aline Bonami, Marco M. Peloso, and Fulvio Ricci, Boundedness of Bergman projections on tube domains over light cones, Math. Z. 237 (2001), no. 1, 31–59. MR 1836772, DOI 10.1007/PL00004861
- D. Békollé, J. Gonessa, and C. Nana, Lebesgue mixed norm estimates for Bergman projectors: from tube domains over homogeneous cones to homogeneous Siegel domains of type II, arXiv:1703.07854.
- David Békollé, Hideyuki Ishi, and Cyrille Nana, Korányi’s lemma for homogeneous Siegel domains of type II. Applications and extended results, Bull. Aust. Math. Soc. 90 (2014), no. 1, 77–89. MR 3227133, DOI 10.1017/S0004972714000033
- Aline Bonami and Luo Luo, On Hankel operators between Bergman spaces on the unit ball, Houston J. Math. 31 (2005), no. 3, 815–827. MR 2148810
- Aline Bonami and Cyrille Nana, Some questions related to the Bergman projection in symmetric domains, Adv. Pure Appl. Math. 6 (2015), no. 4, 191–197. MR 3403436, DOI 10.1515/apam-2015-5008
- Jean Bourgain and Ciprian Demeter, The proof of the $l^2$ decoupling conjecture, Ann. of Math. (2) 182 (2015), no. 1, 351–389. MR 3374964, DOI 10.4007/annals.2015.182.1.9
- D. Debertol, Besov spaces and boundedness of weighted Bergman projections over symmetric tube domains, Dottorato di Ricerca in Matem. Univ. di Genova, Politecnico di Torino, 2003.
- Jacques Faraut and Adam Korányi, Analysis on symmetric cones, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1994. Oxford Science Publications. MR 1446489
- G. Garrigós and A. Seeger, Plate decompositions for cone multipliers, Hokkaido Univ. Math. Report Ser. 103 (2005), 13–28.
- J. Gonessa, Espaces de type Bergman dans les domaines homogènes de Siegel de type II: Décomposition atomique des espaces de Bergman et interpolation, Ph. D. Thesis, Univ. Yaoundé I, 2006.
- M. Seetharama Gowda, Nonfactorization theorems in weighted Bergman and Hardy spaces on the unit ball of $\textbf {C}^{n}$ $(n>1)$, Trans. Amer. Math. Soc. 277 (1983), no. 1, 203–212. MR 690048, DOI 10.1090/S0002-9947-1983-0690048-9
- Charles Horowitz, Factorization theorems for functions in the Bergman spaces, Duke Math. J. 44 (1977), no. 1, 201–213. MR 427650
- Daniel H. Luecking, Embedding theorems for spaces of analytic functions via Khinchine’s inequality, Michigan Math. J. 40 (1993), no. 2, 333–358. MR 1226835, DOI 10.1307/mmj/1029004756
- Cyrille Nana and Benoît Florent Sehba, Carleson embeddings and two operators on Bergman spaces of tube domains over symmetric cones, Integral Equations Operator Theory 83 (2015), no. 2, 151–178. MR 3404692, DOI 10.1007/s00020-014-2210-5
- Jordi Pau and Ruhan Zhao, Carleson measures and Toeplitz operators for weighted Bergman spaces on the unit ball, Michigan Math. J. 64 (2015), no. 4, 759–796. MR 3426615, DOI 10.1307/mmj/1447878031
- Jordi Pau and Ruhan Zhao, Weak factorization and Hankel forms for weighted Bergman spaces on the unit ball, Math. Ann. 363 (2015), no. 1-2, 363–383. MR 3394382, DOI 10.1007/s00208-015-1176-1
- Benoit F. Sehba, Bergman-type operators in tubular domains over symmetric cones, Proc. Edinb. Math. Soc. (2) 52 (2009), no. 2, 529–544. MR 2506404, DOI 10.1017/S0013091506001593
Bibliographic Information
- C. Nana
- Affiliation: Department of Mathematics, Faculty of Science, University of Buea, P. O. Box 63, Buea Cameroon
- Email: nana.cyrille@ubuea.cm
- B. F. Sehba
- Affiliation: Department of Mathematics, University of Ghana, P. O. Box LG 62 Legon, Accra, Ghana
- Email: bfsehba@ug.edu.gh
- Received by editor(s): March 8, 2017
- Published electronically: June 4, 2019
- © Copyright 2019 American Mathematical Society
- Journal: St. Petersburg Math. J. 30 (2019), 723-750
- MSC (2010): Primary 30H20
- DOI: https://doi.org/10.1090/spmj/1567
- MathSciNet review: 3851374