Press "Enter" to skip to content

Reports AIAS. Vol. 22, no 1. P. 32-38. ISSN 1726-9946

Reports AIAS. Vol. 22, no 1. P. 32-38. ISSN 1726-9946

Contents of this issue

DOI: 10.47928/1726-9946-2022-22-1-32-38

MATHEMATICS

MSC 32A10; 32A37 Research Article

On traces of new BMOA type spaces in tubular domains over symmetric cones

 

Shamoyan R. F., Mihi´c O. R.
Presented by full member of AIAS N. L. Pachulia

Bryansk State Technical University, Bryansk, Russia
University of Belgrade, Belgrade, Serbia
E-mail: rshamoyaan@gmail.com, oliveradj@fon.rs

    We provide new sharp trace theorems in new BMOA type analytic function spaces in tubular domains over symmetric cones under certain condition on the Bergman kernel. We obtain based on known properties of r-lattices in tubular domains complete analogues of our previously known results obtained previously by the authors in the unit ball and then in bounded strongly pseudoconvex domains with smooth boundary. Proofs of all theorems in all domains are based mainly on same ideas.

Keywords: analytic function, BMOA type space, tubular domains, trace theorems.

© R. F. Shamoyan,
O. R. Mihi´c, 2022

References

1. Abate M., Saracco A. Carleson measures and uniformly discrete sequences in strongly pseudoconvex domains // Journal of the London Mathematical Society. 2011. Vol. 83, no. 3. P. 587–605.
2. Abate M., Raissy J., Saracco A. Toeplitz operators and Carleson measures in strongly pseudoconvex domains // Journal of Functional Analysis. 2012. Vol. 263, no. 11. P. 3449–3491.
3. Andersson M., Carlsson H. Qp spaces in strictly pseudoconvex domains // Journal d’Analyse Math`ematique. 2001. Vol. 84, no. 1. P. 335–359.
4. Bekolle D., Bonami A., Garrigos G., Nana C., Peloso M., Ricci F. Lecture notes on Bergman projectors in tube domain over cones, an analytic and geometric viewpoint // Proceeding of the International Workshop on Classical Analysis. Yaounde. 2001.
5. Debertol D. Besov spaces and boundedness of weighted Bergman projections over symmetric tube domains // Publicacions Matem`atiques. 2005. Vol. 49, no. 1. P. 21–72.
6. Djrbashian A. E., Shamoian F. A. Topics in the theory of A p \alpha spaces. Leipzig, Teubner, 1988.
7. Faraut J., Koranyi A. Analysis on symmetric cones. Oxford University Press, New York, 1994. xii + 382 p. ISBN: 0-19-853477-9.
8. Ortega J., Fabrega J. Mixed norm spaces and interpolation // Studia Matematica. 1994. Vol. 109, no. 3. P. 233–254.
9. Rudin W. Function theory in the polydisk. New York, 1969.
10. Sehba B. F., Nana C. Carleson Embeddings and two operators on Bergman spaces of tube domains over symmetric cones // Integral Equations and Operator Theory. 2015. Vol. 83, no. 2. P. 151–178.
11. Sehba B. Hankel operators on Bergman spaces of tube domains over symmetric cones // Integral Equations and Operator Theory. 2008. Vol. 62, no. 2. P. 233–245.
12. Sehba B. Operators in some analytic function spaces and their dyadic counterparts. PhD dissertation. University of Glasgow, 2009.
13. Sehba B. Bergman-type integral operators in tube domains over symmetric cones // Proceedings of the Edinburgh Mathematical Society, 2009. Vol. 52. P. 529–544.
14. Shamoyan R., Mihi´c O. On traces of Qp type spaces and mixed norm analytic function spaces on polyballs // Siauliai Mathematical Seminar. 2010. Vol. 5, no. 13. P. 101–119.
15. Shamoyan R. F., Mihi´c O. On a sharp trace theorem in BMOA type spaces in pseudoconvex domains // Comptes Rendus de L’Academie Bulgare des Sciences. 2017. Vol. 70, no. 2. P. 161–166.
16. Xiao J. Geometric QP functions. Birkh¨auser Verlag, 2006. 241 p.
17. Zhu K. Spaces of Holomorphic functions in the unit ball. Part of the Graduate Texts in Mathematics book series. Springer, New York, 2005. 274 p.

Для цитирования. Shamoyan R. F., Mihi´c O. R. On traces of new BMOA type spaces in tubular domains over symmetric cones // Reports of AIAS. 2022. Vol. 22, no. 1. P. 32–38. DOI: 10.47928/1726-9946-2022-22-1-32-38

Read article

©​ | 2022 | Адыгская (Черкесская) Международная академия наук