Нажмите "Enter", чтобы перейти к контенту

Доклады АМАН. Т. 21, №3. С. 21-33. ISSN 1726-9946

Доклады АМАН. Т. 21, №3. С. 21-33. ISSN 1726-9946

Содержание выпуска/Contents of this issue

DOI: 10.47928/1726-9946-2021-21-3-21-33

МАТЕМАТИКА

УДК 517.55+517.33 Научная статья

On some new sharp embedding theorems for multifunctional Herz-type and Bergman-type spaces in tubular domains over symmetric cones

1Shamoyan R.F., 2Tomashevskaya E.B.

Представлено академиком АМАН Н.Л. Пачулиа

Брянский государственный технический университет, Брянск
E-mail: 1rshamoyaan@gmail.com; 2Tomele@mail.ru  

        В работе вводится новый многофункциональный аналитический тип Герца со смешанной нормой пространства в трубчатых областях над симметричными конусами и приводятся для них новые точные теоремы вложения. Некоторые результаты являются новыми даже в случае однофункциональных голоморфных пространств. Некоторые новые связанные точные результаты для новых многофункциональных пространств типа Бергмана будут также предоставлены при одном условии на ядро Бергмана.

Ключевые слова: пространства Бергмана, пространства Герца, трубчатые области над симметричными конусами, теоремы вложения, аналитические функции.

© Р.Ф. Шамоян,
Е.Б. Томашевская, 2021

MATHEMATICS

Research Article

On some new sharp embedding theorems for multifunctional Herz-type and Bergman-type spaces in tubular domains over symmetric cones

1Shamoyan R.F., 2Tomashevskaya E.B.

Presented by academician of AIAS N.L. Patchulia

Bryansk State Technical University, Bryansk
E-mail: 1rshamoyaan@gmail.com; 2Tomele@mail.ru

      We introduce new multifunctional mixed norm analytic Herz-type spaces in tubular domains over symmetric cones and provide new sharp embedding theorems for them. Some results are new even in case of onefunctional holomorphic spaces. Some new related sharp results for new multifunctional Bergman-type spaces will be also provided under one condition on Bergman kernel.

Keywords: Bergman spaces, Herz spaces, tubular domains over symmetric cones, embedding theorems, analytic functions.

© R.F. Shamoyan,
E.B. Tomashevskaya, 2021

Список литературы (ГОСТ)

1. Abate M., Raissy J., Saracco A. Toeplitz operators and Carleson measures in strongly pseudoconvex domains // Journal of Functional Analysis, 2012, vol. 263, no. 11, pp. 3449-3491.
2. Abate M., Saracco A. Carleson measures and uniformly discrete sequences in strongly pseudoconvex domains // J. London Math. Soc., 2011, vol. 83, pp. 587-605.
3. Arsenovi´c M., Shamoyan R.F. On embeddings, traces and multipliers in harmonic function spaces. arXiv:1108.5343
4. Arsenovi´c M., Shamoyan R.F. Embedding theorems for harmonic multifunctional spaces on Rn+1. arXiv:1109.2419
5. Beatrous F. Lp estimates for extensions of holomorphic functions // Michigan Math. Journal, 1985, 32(3), pp. 361-380.
6. Bekolle D., Berger C., Coburn L., Zhu K. BMO in the Bergman metric on bounded symmetric domains // Journal of Functional Analysis, 1990, vol. 93, no. 2, pp. 310-350.
7. Cohn W. Weighted Bergman projection and tangential area integrals // Studia Math., 1993, 106(1), pp. 121-150.
8. Cima J., Mercer P. Composition operators between Bergman spaces in convex domains in Cn // Journal of Operator theory, 1995, vol. 33, no. 2, pp. 363-369.
9. Carleson L. Interpolations by bounded analytic function and the corona problem // Annals of Mathematics, 1962, pp. 547-559.
10. Duren P.L. Extension of a theorem of Carleson // Bull. Amer. Math. Soc., 1969, vol. 75, no. 1, pp. 143-146.
11. Englis M., H¨anninen T., Taskinen J. Minimal L-infinity-type spaces on strictly pseudoconvex domains on which the Bergman projection is continuous // Houston Journal of Mathematics, 2006, 32(1), pp. 253-275.
12. Hastings W.W. A Carleson measure theorem for Bergman spaces // Proc. Am. Math. Soc., 1975, vol. 52, pp. 237-241.
13. H¨ormander L. An introduction to complex analysis in several variables. North Holland. Amsterdam, 1973.
14. Luecking D. A technique for characterizing Carleson measures on Bergman spaces // Proc. Amer. Math. Soc., 1983, vol. 87, pp. 656-660.
15. Mercer P., Cima J. Composition operators between Bergman spaces on convex domains in Cn // Journal of Operator Theory, 1995, 33(2), pp. 363-369.
16. Oleinik V.L., Pavlov B.S. Embedding theorems for weighted classes of harmonic and analytic functions // Journal of Mathematical Sciences, 1974, 2(2), pp. 135-142.
17. Oleinik V.L. Embeddings theorems for weighted classes of harmonic and analytic functions // Journal Soviet Math., 1978, vol. 9, pp. 228-243.
18. Ortega J., Fabrega J. Mixed-norm spaces and interpolation // Studia Math., 1994, vol. 109, no. 3, pp. 234-254.
19. Rudin W. Function theory in the unit ball of Cn. Springer-Verlag. Berlin, 1980. 20. Shamoyan R.F. On some characterizations of Carleson type measure in the unit ball // Banach J. Math. Anal., 2009, vol. 3, no. 2, pp. 42-48.
21. Shamoyan R.F., Kurilenko S. On a new embedding theorem in analytic Bergman type spaces in bounded strictly pseudoconvex domains of n-dimensional complex space // Journal of Siberian Federal University. Mathematics and Physics, 2014, vol. 7, no. 3, pp. 383-388.
22. Shamoyan R.F., Maksakov S.P. Embedding theorems for weighted anisotropic spaces of holomorphic functions in strongly pseudoconvex domains // Romai Journal, 2017, vol. 1, no. 13, pp. 71-92.
23. Shamoyan R.F., Mihi´c O. Embedding theorems for weighted anisotropic spaces of holomorphic functions in tubular domains // Romai J., 2017, 1(13), pp.93-115.
24. Shamoyan R.F., Mihi´c O. On some new sharp estimates in analytic Herz-type function spaces in tubular domains over symmetric cones // Czechoslovak Math. J., 2018, DOI: 10.21136/CMJ.2018.0059-17.
25. Shamoyan R.F., Povpritz E. Multifunctional analytic spaces and new sharp embedding theorems in strongly pseudoconvex domains // Krag. Math. J., 2013, vol. 37, pp. 221-244.
26. Wogen W.R., Cima J.A. A Carleson measure theorem for the Bergman space on the ball // Journal Operator Theory, 1982, vol. 7, pp. 157-165.
27. Zhu K. Spaces of holomorphic functions in the unit ball. Springer-Verlag, New York, 2005.
28. Faraut J., Koranyi A. Analysis on symmetric cones. Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1994, xii + 382 pp. ISBN:0-19-853477-9.
29. Bekolle D., Bonami A., Garrigos G. and others Lecture notes on Bergman projectors in tube domains over cones // Yaounde: Proceedings of the international Workshop on classical Analysis, 2001, 75 p.
30. Debertol D. Besov spaces and boundedness of weighted Bergman projections over symmetric tube domains. Dottorato di Ricerca in Matematica, Universita di Genova, Politecnico di Torino (April), 2003.
31. Sehba B. Bergman-type integral operators in tube domains over symmetric cones // Proceedings of Edinburg Math. Soc.
32. Duren P., Schuster A. Bergman spaces // Mathematical Surveys and Monographs, vol. 100, AMS, RI, 2004.
33. Arsenovi´c M., Shamoyan R. On some extremal problems in spaces of harmonic functions // ROMAI Journal, 2011, vol. 7, pp. 13-34.
34. Shamoyan R.F., Mihi´c O. On new estimates for distances in analytic function spaces in the unit disc, polydisc and unit ball // Bollet. de la Asoc. Matematica Venezolana, 2010, vol. 42, no. 2, pp. 89-103.
35. Shamoyan R., Mihi´c O. On new estimates for distances in analytic function spaces in higher dimension // Siberian Electronic Mathematical Reports, 2009, vol. 6, pp. 514-517.
36. Sehba B. Operators in some analytic function spaces and their dyadic counterparts. Glasgow, PhD, Dissertation, 2009.
37. Sehba B. Hankel operators on Bergman spaces of tube domains over symmetric cones // Integr. eq operator theory, 2008, vol. 62, pp. 233-245.
38. 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, 75 p.
39. Sehba B.F., Nana C. Carleson Embeddings and two operators on Bergman spaces of tube domains over symmetric cones // Integr. Equ. Oper. Theory, 2015, vol. 83, pp. 151-178.
40. Arsenovic M., Shamoyan R. Bergman projection in tube domains over symmetric cones. Filomat, 2011.

Для цитирования. Shamoyan R.F., Tomashevskaya E.B. On some new sharp embedding theorems for multifunctional Herz-type and Bergman-type spaces in tubular domains over symmetric cones // Докл.  Адыгской (Черкесской) международной академии наук. 2021. Т. 21, № 3. C. 21-33. DOI: 10.47928/1726-9946-2021-21-3-21-33
For citation. Shamoyan R.F., Tomashevskaya E.B. On some new sharp embedding theorems for multifunctional Herz-type and Bergman-type spaces in tubular domains over symmetric cones. Reports Adyghe (Circassian) International Academy of Sciences. 2021, vol. 21, no. 3, pp.  21-33. DOI: 10.47928/1726-9946-2021-21-3-21-33

Читать статью/Read article

©​ | 2020 | Адыгская (Черкесская) Международная академия наук