On Bergman type projections in new analytic spaces in tubular domains over symmetric cones
https://doi.org/10.25587/2411-9326-2024-3-73-81
Аннотация
We provide new results on the Bergman type projections in products of tubular domains over symmetric cones extending some known classical assertions. Similar results with the same proof may be valid in the Siegel domains and bounded strongly pseudoconvex domains with smooth boundary. Our new Bergman projection theorems may have various interesting applications in function theory in tubular domains over symmetric cones.
Об авторах
R. F. Shamoyan
Bryansk State Technical University
Россия
Россия
Romy F. Shamoyan
43 Bezhitskaya Street, Bryansk 241050
E. B. Tomashevskaya
Bryansk State Technical University
Россия
Россия
Elena B. Tomashevskaya
43 Bezhitskaya Street, Bryansk 241050
Список литературы
1. Sehba B., “Bergman-type operators in tubular domains over symmetric cones,” Proc. Edinb. Math. Soc., II Ser., 52, No. 2, 529–544 (2009).
2. Duren P. and Schuster A., Bergman Spaces, Amer. Math. Soc., Providence, RI (2004) (Math. Surv. Monogr.; vol. 100).
3. Sehba B., “Operators in some analytic function spaces and their dyadic counterparts,” PhD Thes., Univ. Glasgow, Glasgow (2009).
4. Sehba B., “Hankel operators on Bergman spaces of tube domains over symmetric cones,” Integral Equations Oper. Theory, 62, 233–245 (2008).
5. Bekolle D., Bonami A., Garrigos G., Nana C., Peloso M., and Ricci F., “Lecture notes on Bergman projectors in tube domain over cones, an analytic and geometric viewpoint,” IMHOTEP, J. Afr. Math. Pures Appl., 5 (2004).
6. Sehba B. F. and Nana C., “Carleson embeddings and two operators on Bergman spaces of tube domains over symmetric cones,” Integral Equations Oper. Theory, 83, 151–178 (2015).
7. Arsenovic M. and Shamoyan R., “Embedding relations and boundedness of the Bergman projection in tube domains over symmetric cones,” Filomat, 25, No. 4, 109–126 (2011).
8. Faraut J. and Koranyi A., Analysis on Symmetric Cones, Oxford Univ. Press, New York (1994).
9. Debertol D., “Besov spaces and boundedness of weighted Bergman projections over symmetric tube domains,” Publ. Mat., Barc., 49, No. 1, 21–72 (2005).
10. Zhu K., Spaces of Holomorphic Functions in the Unit Ball, Springer, New York (2005).
11. Shamoyan R. F. and Mihi´ c O. R., “Embedding theorems for weighted anisotropic spaces of holomorphic functions in tubular domains,” ROMAI J., 13, No. 1, 93–115 (2017).
12. Shamoyan R. F. and Mihi´ c O. R., “On some new sharp estimates in analytic Herz-type function spaces in tubular domains over symmetric cones,” Czech. Math. J., 68, No. 4, 1033–1050 (2018).
13. Shamoyan R. F. and Kurilenko S., “On a new embedding theorem in analytic Bergman type spaces in bounded strictly pseudoconvex domains of an n-dimensional complex space,” J. Sib. Fed. Univ., Math. Phys., 7, No. 3, 383–388 (2014).
14. Yaroslavceva O., “Bounded projections and bounded linear functionals in mixed norm spaces of analytic functions in the unit polydisk [in Russian],” Diss. . . . Kand. Fiz.-Mat. Nauk, Bryansk (1999).
15. Mihi´c O. R. and Shamoyan R., “On some new analytic function spaces in polyball,” Palest. J. Math., 4, No. 1, 105–107 (2015).
Рецензия
Для цитирования:
Shamoyan R.F., Tomashevskaya E.B. On Bergman type projections in new analytic spaces in tubular domains over symmetric cones. Математические заметки СВФУ. 2024;31(3):73-81. https://doi.org/10.25587/2411-9326-2024-3-73-81
For citation:
Shamoyan R.F., Tomashevskaya E.B. On Bergman type projections in new analytic spaces in tubular domains over symmetric cones. Mathematical notes of NEFU. 2024;31(3):73-81. (In Russ.) https://doi.org/10.25587/2411-9326-2024-3-73-81
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