Sharp theorems on traces in analytic spaces in tube domains over symmetric cones
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 4, pp. 527-538.

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New sharp estimates of Traces in Bergman-type spaces of analytic functions on tube domains over symmetric cones are obtained. These are first results of this type for tube domains over symmetric cones.
Keywords: trace estimates, analytic functions, Bergman-type spaces.
Mots-clés : tube domains
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Romi F. Shamoyan; Elena Povprits. Sharp theorems on traces in analytic spaces in tube domains over symmetric cones. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 4, pp. 527-538. http://geodesic.mathdoc.fr/item/JSFU_2013_6_4_a13/

[1] M. Arsenović, R. Shamoyan, “Trace theorems in harmonic function spaces, multiplier theorems and related estimates”, Kragujevac Math. Journal, 35:3 (2011), 411–430 | MR | Zbl

[2] R. F. Shamoyan, O. Mihic, “On traces of holomorphic functions in polyballs”, Applicable Analysis and Discrete Mathematics, 3 (2009), 42–48 | DOI | MR | Zbl

[3] R. Shamoyan, O. Mihic, “In search of traces of some holomorphic function spaces in polyballs”, Revista Notas de Matematicas, 1:4 (2008), 1–23 | MR

[4] R. Shamoyan, O. Mihic, “A note on traces of some holomorphic functions classes on polyballs”, Journal of Function Spaces and Applications, 8:3 (2010), 271–285 | DOI | MR | Zbl

[5] R. Shamoyan, O. Mihic, “On some inequalities in holomorphic function theory related to diagonal mapping”, Chechoslovac Mathematical Journal, 60:2 (2010), 351–370 | DOI | MR | Zbl

[6] R. Shamoyan, O. Mihic, “On traces of $Q_p$ type spaces and mixed norm analytic function spaces in polyballs”, Siauliau Math. Seminar, 13:5 (2010), 10–119 | MR

[7] D. Bekolle, A. Bonami, G. Garrigos, C. Nana, M. Peloso, F. Ricci, “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

[8] D. Bekolle, A. Bonami, G. Garrigos, F. Ricci, “Littlewood–Paley decomposition and Besov spaces related to symmetric cones”, Proceedings of London Mathematical Society, 89:2 (2004), 317–360 | DOI | MR | Zbl

[9] D. Bekolle, A. Bonami, G. Garrigos, F. Ricci, B. Sehba, “Analytic Besov spaces and Hardy type inequalities in tube domains over symmetric cones”, Jour. fur reine und ang. mat., 647 (2010), 25–56 | MR | Zbl

[10] W. Rudin, Function theory in polydisk, Benjamin, New York, 1969 | MR | Zbl

[11] M. Jevtic, M. Pavlovic, R. Shamoyan, “A note on diagonal mapping theorem in spaces of analytic functions in the polydisk”, Publ. Math. Debrechen, 74 (2009), 1–14 | MR

[12] G. Ren, J. Shi, “The diagonal mapping in mixed norm spaces”, Studia Math., 163:2 (2004), 103–117 | DOI | MR | Zbl

[13] P. Duren, A. Schuster, Bergman spaces, Mathematical Surveys and Monographs, 100, AMS, Providence, RI, 2004 | DOI | MR | Zbl

[14] M. Djrbashian, F. Shamoyan, Topics in the theory of Bergman $A^p_\alpha$ spaces, Teubner Texte zur Math., 105, Leipzig, 1988 | MR

[15] D. Clark, “Restriction of $H_p$ functions in the polydisk”, Americ. Journal of Mathematics, 110 (1988), 1119–1152 | DOI | MR | Zbl

[16] E. Amar, C. Menini, “A counterexample to the corona theorem for operators in $H^2$ in polydisk”, Pacif. Journal of Mathematics, 206:2 (2002), 257–268 | DOI | MR | Zbl

[17] J. Faraut, A. Koranyi, Analysis on symmetric cones, Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1994 | MR | Zbl

[18] D. Debertol, 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

[19] B. F. Sehba, “Bergman type operators in tube domains over symmetric cones”, Proc. Edinburg. Math. Society (2), 52:2 (2009), 529–544 | DOI | MR | Zbl

[20] B. F. Sehba, “Hankel operators on Bergman Spaces of Tube domains over symmetric cones”, Integr. Equ. Oper. Theory, 62:2 (2008), 233–245 | DOI | MR | Zbl

[21] R. Shamoyan, Sharp theorems for traces in bounded strictly pseudoconvex domains, Preprint, 2012