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ON DISTANCE ESTIMATES AND ATOMIC DECOMPOSITIONS IN SPACES OF ANALYTIC FUNCTIONS ON STRICTLY PSEUDOCONVEX DOMAINS
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 Title & Authors
ON DISTANCE ESTIMATES AND ATOMIC DECOMPOSITIONS IN SPACES OF ANALYTIC FUNCTIONS ON STRICTLY PSEUDOCONVEX DOMAINS
Arsenovic, Milos; Shamoyan, Romi F.;
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 Abstract
We prove some sharp extremal distance results for functions in various spaces of analytic functions on bounded strictly pseudoconvex domains with smooth boundary. Also, we obtain atomic decompositions in multifunctional Bloch and weighted Bergman spaces of analytic functions on strictly pseudoconvex domains with smooth boundary, which extend known results in the classical case of a single function.
 Keywords
Bergman spaces;Bloch space;pseudoconvex domains;extremal problems;atomic decomposition;
 Language
English
 Cited by
1.
On some new sharp embedding theorems in minimal and pseudoconvex domains, Czechoslovak Mathematical Journal, 2016, 66, 2, 527  crossref(new windwow)
 References
1.
M. Abate, J. Raissy, and A. Saracco, Toeplitz operators and Carleson measures in strongly pseudoconvex domains, J. Funct. Anal. 263 (2012), no. 11, 3449-3491. crossref(new window)

2.
P. Ahern and R. Schneider, Holomorphic Lipschitz functions in pseudoconvex domains, Amer. J. Math. 101 (1979), no. 3, 543-565. crossref(new window)

3.
F. Beatrous, Jr. $L^p$-estimates for extensions of holomorphic functions, Michigan Math. J. 32 (1985), no. 3, 361-380. crossref(new window)

4.
W. S. Cohn, Weighted Bergman projections and tangential area integrals, Studia Math. 106 (1993), no. 1, 59-76.

5.
R. Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in $L^p$, Representation theorems for Hardy spaces, pp. 11-66, Asterisque, 77, Soc. Math. France, Paris, 1980.

6.
Z. Cuckovic and J. D. McNeal, Special Toeplitz operators on strongly pseudoconvex domains, Rev. Mat. Iberoam. 22 (2006), no. 3, 851-866.

7.
P. Duren, Theory of $H^p$ Spaces, Academic Press, 1970.

8.
N. Kerzman and E. M. Stein, The Szego kernel in terms of Cauchy-Fantappie kernels, Duke Math. J. 45 (1978), no. 2, 197-223. crossref(new window)

9.
S. Li and W. Luo, On characterization of Besov space and application. Part I, J. Math. Anal. Appl. 310 (2005), 477-491. crossref(new window)

10.
S. Li and W. Luo, Analysis on Besov spaces. II. Embedding and duality theorems, J. Math. Anal. Appl. 333 (2007), no. 2, 1189-1202. crossref(new window)

11.
S. Li and R. Shamoyan, On some extensions of theorems on atomic decompositions of Bergman and Bloch spaces in the unit ball and related problems, Complex Var. Elliptic Equ. 54 (2009), no. 12, 1151-1162. crossref(new window)

12.
S. Li and R. Shamoyan, On some estimates and Carleson type measure for multifunctional holomorphic spaces in the unit ball, Bull. Sci. Math. 134 (2010), no. 2, 144-154. crossref(new window)

13.
E. Ligocka, On the Forelli-Rudin construction and weighted Bergman projections, Studia Math. 94 (1989), no. 3, 257-272.

14.
J. M. Ortega and J. Fabrega, Mixed-norm spaces and interpolation, Studia Math. 109 (1994), no. 3, 233-254.

15.
M. M. Peloso, Hankel operators on weighted Bergman spaces on strongly pseudoconvex domains, Illinois J. Math. 38 (1994), no. 2, 223-249.

16.
R. M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Graduate Texts in Mathematics, 108. Springer-Verlag, New York, 1986.

17.
R. F. Shamoyan, Some remarks on the action of Lusin area operator in Bergman spaces of the unit ball, Acta Univ. Apulensis Math. Inform. 29 (2012), 31-45.

18.
R. F. Shamoyan and M. Arsenovic, Some remarks on extremal problems in weighted Bergman spaces of analytic functions, Commun. Korean Math. Soc. 27 (2012), no. 4, 753-762, crossref(new window)

19.
R. Shamoyan and O. Mihic, On new estimates for distances in analytic function spaces in higher dimension, Sib. Elektron. Mat. Izv. 6 (2009), 514-517.

20.
R. Shamoyan and O. Mihic, On new estimates for distances in analytic function spaces in the unit disk, the polydisk and the unit ball, Bol. Asoc. Mat. Venez. 17 (2010), no. 2, 89-103.

21.
K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Springer-Verlag, New York, 2005.