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On some extremal problems in Bergman spaces in weakly pseudoconvex domains
Communications in Mathematics, Tome 26 (2018) no. 2, pp. 83-97 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We consider and solve extremal problems in various bounded weakly pseudoconvex domains in $\mathbb {C}^{n}$ based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces $A_{\alpha }^{p}$ in such type domains. We provide some new sharp theorems for distance function in Bergman spaces in bounded weakly pseudoconvex domains with natural additional condition on Bergman representation formula.
We consider and solve extremal problems in various bounded weakly pseudoconvex domains in $\mathbb {C}^{n}$ based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces $A_{\alpha }^{p}$ in such type domains. We provide some new sharp theorems for distance function in Bergman spaces in bounded weakly pseudoconvex domains with natural additional condition on Bergman representation formula.
Classification : 42B15, 42B30
Keywords: Bergman spaces; distance estimates; pseudoconvex domains; analytic functions 
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Shamoyan, Romi F.; Mihić, Olivera R. On some extremal problems in Bergman spaces in weakly pseudoconvex domains. Communications in Mathematics, Tome 26 (2018) no. 2, pp. 83-97. http://geodesic.mathdoc.fr/item/COMIM_2018_26_2_a0/

[1] Ahn, H., Cho, S.: On the mapping properties of the Bergman projection on pseudoconvex domains with one degenerate eigenvalue. Complex Variables Theory Appl., 39, 4, 1999, 365-379, | DOI | MR

[2] Arsenović , M., Shamoyan, R.: On distance estimates and atomic decomposition on spaces of analytic functions on strictly pseudoconvex domains. Bulletin Korean Math. Society, 52, 1, 2015, 85-103, | MR

[3] Beatrous, F.: Estimates for derivatives of holomorphic functions in strongly pseudoconvex domains. Math. Zam., 191, 1, 1986, 91-116, | DOI | MR

[4] Charpentier, P., Dupain, Y.: Estimates for the Bergman and Szegö projections for pseudoconvex domains of finite type with locally diagonalizable Levi form. Publ. Mat., 50, 2006, 413-446, | DOI | MR

[5] Chen, B.: Weighted Bergman kernel: asymptotic behavior, applications and comparison results. Studia Mathematica, 174, 2, 2006, 111-130, | DOI | MR

[6] Cho, H.R., Kwon, E.G.: Embedding of Hardy spaces into weighted Bergman spaces in bounded domains with $C^2$ boundary. Illinois J. Math., 48, 3, 2004, 747-757, | DOI | MR

[7] Cho, S.: A mapping property of the Bergman projection on certain pseudoconvex domains. Tóhoku Math. Journal, 48, 1996, 533-542, | DOI | MR

[8] Ehsani, D., Lieb, I.: $L^p$-estimates for the Bergman projection on strictly pseudoconvex nonsmooth domains. Math. Nachr., 281, 7, 2008, 916-929, | DOI | MR

[9] Gheorghe, L.G.: Interpolation of Besov spaces and applications. Le Matematiche, LV, Fasc. I, 2000, 29-42, | MR

[10] Jevtić, M.: Besov spaces on bounded symmetric domains. Matematički vesnik, 49, 1997, 229-233, | MR

[11] Lanzani, L., Stein, E.M.: The Bergman projection in $L^p$ for domains with minimal smoothness. Illinois Journal of Mathematics, 56, 1, 2012, 127-154, | DOI | MR

[12] McNeal, J.D., Stein, E.M.: Mapping properties of the Bergman projection on convex domain of finite type. Duke Math. J., 73, 1994, 177-199, | MR

[13] Phong, D.H., Stein, E.M.: Estimates for the Bergman and Szegö projection on strongly pseudoconvex domains. Duke Math. J., 44, 1977, 695-704, | MR

[14] Shamoyan, R.F., Kurilenko, S.M.: On extremal problems in tubular domains over symmetric cones. Issues of Analysis, 1, 2014, 44-65, | DOI | MR

[15] Shamoyan, R.F., Mihić , O.: Extremal Problems in Certain New Bergman Type Spaces in Some Bounded Domains in $\mathbb {C}^{n}$. Journal of Function Spaces, 2014, 2014, p. 11, Article ID 975434. | MR

[16] Shamoyan, R.F., Mihić, O.: On distance function in some new analytic Bergman type spaces in $\mathbb {C}^{n}$. Journal of Function Spaces, 2014, 2014, p. 10, Article ID 275416. | MR

[17] Shamoyan, R.F., Mihić, O.: On new estimates for distances in analytic function spaces in higher dimension. Siberian Electronic Mathematical Reports, 6, 2009, 514-517, | MR | Zbl

[18] Zhu, K.: Holomorphic Besov spaces on bounded symmetric domains. Quarterly J. Math., 46, 1995, 239-256, | DOI | MR

[19] Zhu, K.: Holomorphic Besov spaces on bounded symmetric domains, III. Indiana University Mathematical Journal, 44, 1995, 1017-1031, | MR