Вестник КРАУНЦ. Физ.-мат. науки. 2020. Т. 32. № 3. C. 102-113. ISSN 2079-6641

Содержание выпуска/Contents of this issue

Research Article

MSC 32A07, 432A10, 32A07 

On new sharp theorems for multifunctional BMOA type spaces in bounded pseudoconvex domains

R. F. Shamoyan¹, E. B. Tomashevskaya²

¹Department of Mathematical Analysis, Bryansk State University named after Academician I. G. Petrovsky, Bryansk, 241036, Bryansk, str. Bezhitskaya, 14, Russia
²Department of Mathematics, Bryansk State Technical University, Bryansk 241050, Russia

E-mail: rsham@mail.ru, tomele@mail.ru

We provide new equivalent expressions in the unit ball and pseudoconvex domains for multifunctional analytic BMOA type space. We extend in various directions a known theorem of atomic decomposition of BMOA type spaces in the unit ball.

Keywords: unit ball, analytic functions, analytic spaces, pseudoconvex domain, Hardy spaces, Bergman spaces, BMOA type spaces

DOI: 10.26117/2079-6641-2020-32-3-102-113

Original article submitted: 30.04.2020

Revision submitted: 08.08.2020

For citation. Shamoyan R. F., Tomashevskaya E. B. On new sharp theorems for multifunctional BMOA type spaces in bounded pseudoconvex domains. Vestnik KRAUNC. Fiz.-mat. nauki. 2020, 32: 3, 102-113. DOI: 10.26117/2079-6641-2020-32-3-102-113

The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)

© Shamoyan R. F., Tomashevskaya E. B., 2020

Научная статья

УДК 517.55+517.33 

О новых точных теоремах разложения для многофункциональных пространств типа ВМОА в ограниченных псевдовыпуклых областях

Р. Ф. Шамоян¹, Е. Б. Томашевская²

¹Брянский государственный университет имени академика И. Г. Петровского, 241036, г. Брянск, Россия
²Брянский государственный технический университет, 241050, г. Брянск, Россия

E-mail: rsham@mail.ru, tomele@mail.ru

Мы приводим новые эквивалентные выражения в единичных шаровых и псевдовыпуклых областях для многофункционального аналитического пространства типа BMOA. Мы расширяем в различных направлениях известную теорему атомарного разложения пространств типа BMOA в единичном шаре.

Ключевые слова: единичный шар, аналитические функции, аналитические пространства, псевдовыпуклая область, пространства Харди, пространства Бергмана, пространства типа BMOA.

DOI: 10.26117/2079-6641-2020-32-3-102-113

Поступила в редакцию: 30.04.2020

В окончательном варианте: 08.08.2020

Для цитирования. Shamoyan R. F., Tomashevskaya E. B. On new sharp theorems for multifunctional BMOA type spaces in bounded pseudoconvex domains // Вестник КРАУНЦ. Физ.-мат. науки. 2020. Т. 32. № 3. C. 102-113. DOI: 10.26117/2079-6641-2020-32-3-102-113

Контент публикуется на условиях лицензии Creative Commons Attribution 4.0 International (https://creativecommons.org/licenses/by/4.0/deed.ru)

© Шамоян Р. Ф., Томашевская Е. Б., 2020

References

1. Abate M., Raissy J., Saracco A., “Toeplitz operators and Carleson measure in strongly pseudoconvex domains”, J. Func. Anal., 263:11 (2012), 3449-3491.
2. Andersson M., Carlsson H., “Qp spaces in strictly pseudoconvex domains”, Journal d’Analyse Mathematique, 84 (2001), 335-359.
3. Arsenovic M., Shamoyan R., “On some sharp estimates for distances in bounded strictly pseudoconvex domains”, Bulletin Korean Math. Society, 52:1 (2015), 85-103.
4. Beatrous F., Jr., “Lp estimates for extensions of holomorphic functions”, Michigan Math. Jour., 32:3 (1985), 361-380.
5. Bekolle D., Bonami A., Garrigos G. and others., Lecture notes on Bergman projectors in tube domains over cones., Procedings of the international Workshop on classical Analysis, Yaounde, 2001, 75 pp.
6. Cohn W. S., “Weighted Bergman projections and tangential area integrals, Studia Math.”, 106:1 (1993), 59-76.
7. Faraut J., Koranyi A., Analysis on symmetric cones, Oxford Mathematical Monographs. V. XII, Oxford University Press, New York, 1994, 382 pp.
8. Krantz S.G., Li S.-Y., “On decomposition theorems for Hardy spaces on domains in Cn and applications”, Jour, Four. Analysis and Applic, 2 (1995), 65-107.
9. Luecking D., “Representations and duality in weighted spaces of analytic functions”, Indiana Univ. Math. Journal, 34:2 (1985), 319-336.
10. Ortega J.M., Fabrega J., “Mixed-norm spaces and interpolations”, Studia Math., 109:3 (1994), 233-254.
11. Range R. M., Holomorphic Functions and Integral Representations in Several Complex Variables, Graduate Texts in Mathematics. V. 108, Springer-Verlag, New York, 1986.
12. Rochberg R., “Decomposition theorems for Bergman spaces and their applications, Operators and function theory (Lancaster 1984)”, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 153 (1985), 225–277.
13. Shamoyan R. F.“On decomposition theorems of multifunctional Bergman type spaces in some domains in Cn”, Vestnik KRAUNC. Fiz.-mat. nauki., 26:1 (2019), 28-45.
14. Shamoyan R. F., Loseva V. V., “On Hardy type spaces in some domains in Cn and related problems”, Vestnik KRAUNC. Fiz.-mat. nauki, 27:2 (2019), 12–37.
15. Shamoyan R.F., Tomashevskaya E.B.“On some new decomposition theorems in multifunctional Herz and Bergman analytic function spaces in bounded pseudoconvex domains”, Vestnik KRAUNC. Fiz.-mat. nauki, 30:1 (2020), 42-58.
16. Shamoyan R. F., Tomashevskaya E. B.“On New Decomposition Theorems in some Analytic Function Spaces in Bounded Pseudoconvex Domains”, Journal of Siberian Federal University, Mathematics and Physics, 13(4) (2020), 503-514.
17. Zhu K., Spaces of Holomorphic Functions in the unit ball, Springer-Verlag-New York, 2005, 226 pp.

References (GOST)

1. Abate M., Raissy J., Saracco A. Toeplitz operators and Carleson measure in strongly pseudoconvex domains // J. Func. Anal. vol. 263. no. 11. 2012. pp. 3449-3491.
2. Andersson M., Carlsson H. Qp spaces in strictly pseudoconvex domains // Journal d’Analyse Mathematique. vol. 84. 2001. pp. 335-359.
3. Arsenovic M., Shamoyan R. On some sharp estimates for distances in bounded strictly pseudoconvex domains // Bulletin Korean Math. Society. vol. 52. no. 1. 2015. pp. 85-103.
4. Beatrous F., Jr. Lp estimates for extensions of holomorphic functions // Michigan Math. Jour. 1985. vol. 32. no. 3. pp. 361-380.
5. Bekolle D., Bonami A., Garrigos G. and others. Lecture notes on Bergman projectors in tube domains over cones. Yaounde: Procedings of the international Workshop on classical Analysis. 2001. 75 c.
6. Cohn W. S. Weighted Bergman projections and tangential area integrals, Studia Math. vol. 106. no. 1. 1993. pp. 59-76.
7. Faraut J., Koranyi A. Analysis on symmetric cones. Oxford Mathematical Monographs. XII. New York: Oxford University Press, 1994. 382 p.
8. Krantz S.G., Li S.-Y. On decomposition theorems for Hardy spaces on domains in Cn and applications // Jour, Four. Analysis and Applic. 1995. vol. 2. pp. 65-107.
9. Luecking D. Representations and duality in weighted spaces of analytic functions // Indiana Univ. Math. Journal. 1985. vol. 34. no. 2. pp. 319-336.
10. Ortega J.M., Fabrega J. Mixed-norm spaces and interpolations // Studia Math. 1994. vol. 109. no. 3. pp. 233-254.
11. Range R. M. Holomorphic Functions and Integral Representations in Several Complex Variables. Graduate Texts in Mathematics. 108. New York: Springer-Verlag, 1986.
12. Rochberg R. Decomposition theorems for Bergman spaces and their applications, Operators and function theory (Lancaster 1984) // NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 1985. vol. 153. pp. 225–277.
13. Shamoyan R. F. On decomposition theorems of multifunctional Bergman type spaces in some domains in Cn // Vestnik KRAUNC. Fiz.-mat. nauki. 2019. vol. 26. no. 1. pp. 28-45.
14. Shamoyan R. F., Loseva V.V. On Hardy type spaces in some domains in Cn and related problems // Vestnik KRAUNC. Fiz.-mat. nauki. 2019. vol. 27. no. 2. pp. 12–37.
15. Shamoyan R.F., Tomashevskaya E.B. On some new decomposition theorems in multifunctional Herz and Bergman analytic function spaces in bounded pseudoconvex domains // Vestnik KRAUNC. Fiz.-mat. nauki. 2020. vol. 30. no. 1. pp. 42-58.
16. Shamoyan R. F., Tomashevskaya E. B. On New Decomposition Theorems in some Analytic Function Spaces in Bounded Pseudoconvex Domains // Journal of Siberian Federal University, Mathematics and Physics. 2020. vol. 13(4). pp. 503-514.
17. Zhu K. Spaces of Holomorphic Functions in the unit ball. Springer-Verlag-New York, 2005. 226 p.

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