Geodesic
Оn a trace operator in Bergman type analytic spaces in Siegel domains of~the second type
Problemy fiziki, matematiki i tehniki, no. 2 (2015), pp. 83-90.

Voir la notice de l'article provenant de la source Math-Net.Ru

A new sharp result for a trace operator in analytic Bergman spaces in products of Siegel domains of the second type extending previously known assertions in less general domains is provided. These are the first results of this type for such a type product-domains.
Keywords: analytic functions, Bergman-type spaces.
Mots-clés : Traces, Siegel domains 
@article{PFMT_2015_2_a13,
     author = {R. F. Shamoyan and S. M. Kurilenko},
     title = {{\CYRO}n a trace operator in {Bergman} type analytic spaces in {Siegel} domains of~the second type},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {83--90},
     publisher = {mathdoc},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2015_2_a13/}
}
TY  - JOUR
AU  - R. F. Shamoyan
AU  - S. M. Kurilenko
TI  - Оn a trace operator in Bergman type analytic spaces in Siegel domains of~the second type
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2015
SP  - 83
EP  - 90
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2015_2_a13/
LA  - en
ID  - PFMT_2015_2_a13
ER  - 
%0 Journal Article
%A R. F. Shamoyan
%A S. M. Kurilenko
%T Оn a trace operator in Bergman type analytic spaces in Siegel domains of~the second type
%J Problemy fiziki, matematiki i tehniki
%D 2015
%P 83-90
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2015_2_a13/
%G en
%F PFMT_2015_2_a13
R. F. Shamoyan; S. M. Kurilenko. Оn a trace operator in Bergman type analytic spaces in Siegel domains of~the second type. Problemy fiziki, matematiki i tehniki, no. 2 (2015), pp. 83-90. http://geodesic.mathdoc.fr/item/PFMT_2015_2_a13/

[1] D. Bekolle, A. T. Kagou, “Reproducing properties and $L^p$ estimates for Bergman projections in Siegel domains of type II”, Studia Math., 15:3 (1995), 219–239 | MR

[2] A. T. Kagou, Domains de Siegel de type II, noyau de Bergman, These de doctorate de 3 eme cycles, Yaounde, 1993

[3] S. Gindikin, “Analysis in homogeneous domains”, Russia Math. Surveys, 19:4 (1964), 1–89 | MR

[4] F. Shamoyan, A. Djrbashian, Topics in the theory of $A_\alpha^p$ spaces, Teubner Texte zur Mathematics, Leipzig, 1988 | MR

[5] W. Rudin, Function theory in polydisks, Academic press, New-York, 1969

[6] R. Shamoyan, “On extremal problems in two Siegel domains”, ROMAI Journal, 8:2 (2012), 167–180 | MR | Zbl

[7] M. Jevtic, M. Pavlovic, R. Shamoyan, “A note on diagonal mapping theorem in spaces of analytic functions in the polydisk”, Publ. Math. Debrechen, 74:1/2 (2009), 1–14 | MR

[8] R. Shamoyan, S. Kurilenko, “On extremal problems in analytic Bergman type spaces in tubular domains over symmetric cones”, Issues of Analysis, 3:21 (2014), 44–65 | Zbl

[9] R. Shamoyan, O. Mihic, “On a new space of analytic functions in polyball”, Palestine Journal, 2014, no. 2, 213–216

[10] R. Shamoyan, O. Mihic, “On trace of holomorphic functions on the unit polyball”, Appl. Anal. Discrete Mathematics, 2009, no. 3, 198–211 | MR | Zbl

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

[12] D. Clark, “Restriction of $H^p$ functions in the polydisk”, American Journal of Mathematics, 110 (1988), 1119–1152 | MR | Zbl

[13] R. Shamoyan, E. Povprits, “Sharp theorems on traces in Bergman type spaces in tubular domains over symmetric cones”, Journal of Siberian Federal University, 6:4 (2013), 527–538

[14] R. Shamoyan, E. Povprits, “Multifunctional analytic spaces products of bounded strictly pseudoconvex domains and embedding theorems”, Kragujevac Mathematical Journal, 37 (2013), 221–244 | MR | Zbl

[15] S.-Y. Chang, R. Fefferman, “Some recent developments in Fourier analysis and $H^p$ theory on product domains”, Bulletin Amer. Math. Society, 12:1 (1985), 1–43 | MR | Zbl

[16] A. Kagou, “The duals of Bergman spaces in Siegel domains of second type”, IMHOTEP, 1 (1997), 38–86 | MR

[17] M. Arsenovic, R. Shamoyan, “On distance estimates and atomic decomposition on spaces of analytic functions on strictly pseudoconvex domains”, Bulletin Korean Mathematical Society, 2 (2014), 314–325 | MR

[18] R. Shamoyan, O. Mihic, “On traces of $\mathcal{Q}_p$ type spaces and mixed norm analytic spaces in polyballs”, Siauliau Mathematical Seminar, 13:5 (2010), 110–119 | MR

[19] D. Bekolle, A. Kagou, “Molecular decomposition and interpolation”, Integral Equations and Operator theory, 31:22 (1998), 150–177 | MR | Zbl

[20] T. Jimb, A. Sakai, “Interpolation manifolds for products of strictly pseudoconvex domains”, Complex Variables, 8 (1987), 222–341 | MR

[21] P. Jakobczak, “The boundary regularity of the solution of the df equation in products of strictly pseudoconvex domains”, Pacific Journal of Mathematics, 121:2 (1986), 371–386 | MR

[22] M. Arsenovic, R. Shamoyan, “On embeddings traces and multipliers in harmonic function spaces”, Kragujevac Math. Journal, 37:1 (2013), 45–65 | MR