Вестник КРАУНЦ. Физ.-мат. науки. 2019. Т. 26. № 1. C. 28-45. DOI: 10.26117/2079-6641-2019-26-1-28-45

Содержание

DOI: 10.26117/2079-6641-2019-26-1-28-45

MSC 32A07, 432A10, 32A07

ON DECOMPOSITION THEOREMS OF MULTIFUNCTIONAL BERGMAN TYPE SPACES IN SOME DOMAINS IN Cn

R. F. Shamoyan

Department of Mathematics, Bryansk State Technical University, Bryansk 241050, Russia
E-mail: rsham@mail.ru

We present some extensions of well-known one functional results on atomic decompositions in classical Bergman spaces obtained earlier by various authors in some new multifunctional Bergman type spaces in various domains in higher dimension.

Keywords: Bergman type spaces, analytic functions, decomposition theorems.

© Shamoyan R. F., 2019

УДК 517.55+517.33

О ТЕОРЕМАХ ДЕКОМПОЗИЦИИ В МУЛЬТИФУНКЦИОНАЛЬНЫХ ПРОСТРАНСТВАХ БЕРГМАНА

Р. Ф. Шамоян

Брянский государственный технический университет, 241050, г. Брянск, Россия

E-mail: rsham@mail.ru

Мы приводим некоторые новые теоремы о декомпозиции аналитических функций из мультифункциональных пространств Бергмана, обобщающие ранее известные результаты подобного типа для обычных пространств Бергмана в различных областях.

Ключевые слова: аналитические функции, пространства Бергмана мультифункциональные пространства, теоремы декомпозиции.

© Шамоян Р. Ф., 2019

Список литературы/References

  1. Coifman R., Rochderg R., “Representation theorems for holomorphic and harmonic functions Lp”, Asterisque, 1980, №77, 11-66.
  2. Rochderg R., Semmes S., “A decomposition theorem for BMO and applications”, Jour. of Func. Analysis., 1986 67, 228-263.
  3. Luecking D., “Representations and duality in weighted spaces of analytic functions”, Indiana Univ. Math. Journal, 34:2 (1985), 319-336.
  4. Li S., Shamoyan R., “O nekotorykh rasshireniyakh teorema ob atomnykh razlozheniyakh prostranstv Bergmana i Blokha v yedinichnom share i svyazannykh s nimi zadachakh [On some extensions of theorems on atomic decompositions of Bergman and Bloch spaces in the unit ball and related problems]”, Zhurnal ellipticheskikh uravneniy i kompleksnykh peremennykh [Journal of Elliptic equations and Complex Variables], 2010 (In Russ.).
  5. Shamoyan R., Arsenovic M., “On distance estimates and atomic decompositions in spaces of analytic functions on stricty pseudoconvex domains”, Bulletin Korean Math. Society, 2015.
  6. Bekolle D., Kagou A. T., “Reproducing properties and Lp estimates for Bergman projections in Siegel domains of second type”, Studia Math., 115:3 (1995).
  7. Bekolle D., Bonami A., Garrigos G., Ricci F., Sehba B. Analytic Besov spaces and symmetric cones, Jour. Fur seine and ang., 2010, №647, 25-56.
  8. Yamaji S., Some properties of Bergman kernel in minimal bounded homogeneous domain, Arxiv, 2013.
  9. Yamaji S., Essential norm estimates for positive Toeplitz operators on the weighted Bergman space, Arxiv, 2013.
  10. Bekolle D., Kagou A., “Molecular decomposition and interpolation”, Int. Equat. Oper. Theory, 31:2 (1998), 150-177.
  11. Bonami A., Bekolle D., Garrigos G., “Lecture notes on Bergman projections in tube domains over symmetric cones”, Yaonde Proc. Int. Workshop, 2001, 75 pp.
  12. Kagou A., Temgoua Domaines de Siegel de type II noyau de Bergman, These de 3 cycle, Yaounde, 1995.
  13. Gheorghi L. G., “Interpolation of Besov spaces and applications”, Le Mathematiche, LV:1 (2000), 29-42.
  14. Zhu K., Spaces of holomorphic functions in the ball, N-Y, Springer, 2005.
  15. Rochberg R., “Decomposition theorems for Bergman spaces and applications”, Operator theory and function theory, 1985, 225-277.
  16. Krantz S., Li S.-Y., “On decomposition theorems for Hardy spaces in domains in Cn and applications”, Journal of Fourier analysis and applications, 1995.
  17. Shamoyan F., “O teoremakh vlozheniya i sledakh Hp prostranstv Khardi na diagonali [On embedding theorems and traces of Hp Hardy spaces on diagonal]”, Matematika Sbornik [Math. Sbornik], 1978 (In Russ.).
  18. Shamoyan F., Djrbashian A., “Temy teorii prostranstv Apa [Topics in the theory of Apa spaces]”, Teubner Texte zur Math., 1988..
  19. Mengotti G., “The Bloch space for minimall ball”, Studia Math., 148:2 (2001), 131-142.

Список литературы (ГОСТ)

  1. Coifman R., Rochderg R. Representation theorems for holomorphic and harmonic functions Lp // Asterisque. 1980. no. 77. pp. 11-66.
  2. Rochderg R., Semmes A decomposition theorem for BMO and applications // Jour. of Func. Analysis. 1986. no. 67. pp. 228-263.
  3. Luecking D. Representations and duality in weighted spaces of analytic functions // Indiana Univ. Math. Journal. 1985. vol. 34. no. 2. pp. 319-336.
  4. Li S., Shamoyan R. O nekotorykh rasshireniyakh teorema ob atomnykh razlozheniyakh prostranstv Bergmana i Blokha v yedinichnom share i svyazannykh s nimi zadachakh [On some extensions of theorems on atomic decompositions of Bergman and Bloch spaces in the unit ball and related problems] // Zhurnal ellipticheskikh uravneniy i kompleksnykh peremennykh [Journal of Elliptic equations and Complex Variables], 2010. (In Russ.)
  5. Shamoyan R., Arsenovic M. On distance estimates and atomic decompositions in spaces of analytic functions on stricty pseudoconvex domains // Bulletin Korean Math. Society, 2015.
  6. Bekolle D., Kagou A. T. Reproducing properties and Lp estimates for Bergman projections in Siegel domains of second type // Studia Math. 1995. vol. 115. no 3.
  7. Bekolle D., Bonami A., Garrigos G., Ricci F., Sehba B. Analytic Besov spaces and symmetric cones // Jour. Fur seine and ang. 2010. no. 647. pp. 25-56.
  8. Yamaji S. Some properties of Bergman kernel in minimal bounded homogeneous domain // Arxiv, 2013.
  9. Yamaji S. Essential norm estimates for positive Toeplitz operators on the weighted Bergman space // Arxiv, 2013.
  10. Bekolle D., Kagou A. Molecular decomposition and interpolation // Int. Equat. Oper. Theory. 1998. vol. 31. no. 2. pp. 150-177.
  11. Bonami A., Bekolle D., Garrigos G. Lecture notes on Bergman projections in tube domains over symmetric cones // Yaonde Proc. Int. Workshop. 2001. 75 p.
  12. Kagou A. Temgoua Domaines de Siegel de type II noyau de Bergman // These de 3 cycle, Yaonde, 1995.
  13. Gheorghi L. G. Interpolation of Besov spaces and applications // Le Mathematiche. 2000. vol. LV. no. 1. pp. 29-42.
  14. Zhu K. Spaces of holomorphic functions in the ball. N-Y: Springer, 2005.
  15. Rochberg R. Decomposition theorems for Bergman spaces and applications // Operator theory and function theory. 1985. pp. 225-277.
  16. Krantz S., Li S.-Y. On decomposition theorems for Hardy spaces in domains in Cn and applications // Journal of Fourier analysis and applications, 1995.
  17. Shamoyan F. O teoremakh vlozheniya i sledakh Hp prostranstv Khardi na diagonali [On embedding theorems and traces of Hp Hardy spaces on diagonal] // Matematika Sbornik [Math. Sbornik]. 1978. (In Russ.)
  18. Shamoyan F., Djrbashian A. Temy teorii prostranstv Apa [Topics in the theory of Apa spaces] // Teubner Texte zur Math., Leipzig, 1988.
  19. Mengotti G. The Bloch space for minimall ball // Studia Math. 2001. vol. 148. no. 2. pp. 131-142.

Для цитирования: Shamoyan R. F On decomposition theorems of multifunctional Bergman type spaces in some domains in Cn // Вестник КРАУНЦ. Физ.-мат. науки. 2019. Т. 26. № 1. C. 28-45. DOI: 10.26117/2079-6641-2019-26-1-28-45
For citation: Shamoyan R. F On decomposition theorems of multifunctional Bergman type spaces in some domains in Cn, Vestnik KRAUNC. Fiz.-mat. nauki. 2019, 26: 1, 28-45. DOI: 10.26117/2079-6641-2019-26-1-28-45

Поступила в редакцию / Original article submitted: 29.10.2018

Shamoyan 

 Шамоян Роми Файзович – кандидат физико-математических наук, старший научный сотрудник кафедры математического анализа, Брянский государственный университет имени академика И. Г. Петровского, Брянск, Россия.
  Shamoyan Romi Fayzovich – Ph.D. (Phys. & Math.), Senior Researcher, Department of Mathematical Analysis, Bryansk State University named after Academician I. G. Petrovsky, Bryansk, Russia.

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