On some extremal problems in Bergman spaces in weakly pseudoconvex domains

Open access

Abstract

We consider and solve extremal problems in various bounded weakly pseudoconvex domains in ℂn based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces Aαp 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.

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

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

[3] F. Beatrous: Estimates for derivatives of holomorphic functions in strongly pseudoconvex domains. Math. Zam. 191 (1) (1986) 91–116.

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

[5] B. Chen: Weighted Bergman kernel: asymptotic behavior, applications and comparison results. Studia Mathematica 174 (2) (2006) 111–130.

[6] H.R. Cho, E.G. Kwon: Embedding of Hardy spaces into weighted Bergman spaces in bounded domains with C2 boundary. Illinois J. Math. 48 (3) (2004) 747–757.

[7] S. Cho: A mapping property of the Bergman projection on certain pseudoconvex domains. Tóhoku Math. Journal 48 (1996) 533–542.

[8] D. Ehsani, I. Lieb: Lp-estimates for the Bergman projection on strictly pseudoconvex nonsmooth domains. Math. Nachr. 281 (7) (2008) 916–929.

[9] L.G. Gheorghe: Interpolation of Besov spaces and applications. Le Matematiche LV (Fasc. I) (2000) 29–42.

[10] M. Jevtić: Besov spaces on bounded symmetric domains. Matematički vesnik 49 (1997) 229–233.

[11] L. Lanzani, E.M. Stein: The Bergman projection in Lp for domains with minimal smoothness. Illinois Journal of Mathematics 56 (1) (2012) 127–154.

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

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

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

[15] R.F. Shamoyan, O. Mihić: Extremal Problems in Certain New Bergman Type Spaces in Some Bounded Domains in ℂn. Journal of Function Spaces 2014 (2014) p. 11. Article ID 975434

[16] R.F. Shamoyan, O. Mihić: On distance function in some new analytic Bergman type spaces in ℂn. Journal of Function Spaces 2014 (2014) p. 10. Article ID 275416

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

[18] K. Zhu: Holomorphic Besov spaces on bounded symmetric domains. Quarterly J. Math. 46 (1995) 239–256.

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

Journal Information

CiteScore 2017: 0.33

SCImago Journal Rank (SJR) 2017: 0.128
Source Normalized Impact per Paper (SNIP) 2017: 0.476

Mathematical Citation Quotient (MCQ) 2017: 0.43

Target Group

researchers in the fields of: algebraic structures, calculus of variations, combinatorics, control and optimization, cryptography, differential equations, differential geometry, fuzzy logic and fuzzy set theory, global analysis, mathematical physics and number theory

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 47 47 26
PDF Downloads 33 33 18