ON SOME PROPERTIES OF HOLOMORPHIC SPACES BASED ON BERGMAN METRIC BALL AND LUZIN AREA OPERATOR

Volume 2, Issue 3, pp 183-194 http://dx.doi.org/10.22436/jnsa.002.03.07

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Authors

ROMI F. SHAMOYAN - Bryansk University, Bryansk, Russia. OLIVERA R. MIHIĆ - Fakultet organizacionih nauka, Jove Ilića 154, Belgrade, Serbia.

Abstract

We provide new estimates and embedding theorems for holomorphic spaces in the unit ball defined with the help of Bergman metric ball and Luzin area operator. We also study the boundedness of integral operators similar to classical Bergman projections on spaces of mentioned type.

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ISRP Style

ROMI F. SHAMOYAN, OLIVERA R. MIHIĆ, ON SOME PROPERTIES OF HOLOMORPHIC SPACES BASED ON BERGMAN METRIC BALL AND LUZIN AREA OPERATOR, Journal of Nonlinear Sciences and Applications, 2 (2009), no. 3, 183-194

AMA Style

SHAMOYAN ROMI F., MIHIĆ OLIVERA R., ON SOME PROPERTIES OF HOLOMORPHIC SPACES BASED ON BERGMAN METRIC BALL AND LUZIN AREA OPERATOR. J. Nonlinear Sci. Appl. (2009); 2(3):183-194

Chicago/Turabian Style

SHAMOYAN , ROMI F., MIHIĆ, OLIVERA R.. " ON SOME PROPERTIES OF HOLOMORPHIC SPACES BASED ON BERGMAN METRIC BALL AND LUZIN AREA OPERATOR." Journal of Nonlinear Sciences and Applications, 2, no. 3 (2009): 183-194

Keywords

weighted Bergman space
Hardy space
inequality
Bergman metric ball.

MSC

32A18

References

[1] A. V. Aleksandrov, Function Theory in the Ball, in Several Complex Variables II, Springer- Verlag, New York (1994)

[2] C. Cascante, J. Ortega, Carleson measures on spaces of Hardy-Sobolev type, Canad. J. Math., 47(6) (1995), 1177-1200

[3] C. Cascante, J. Ortega, On q - Carleson measures for spaces of \(M\)- harmonic functions, Canad. J. Math., 49 (4) (1997), 653-674
- Google Scholar
- MATH

[4] C. Cascante, J. Ortega, Imbedding potentials in tent spaces, J. Funct. Anal., 1 (2003), 106-141

[5] W. Cohn, Generalized area operator on Hardy spaces, Journal of Mathematical Analysis and Applications, 216 (1997), 112-121

[6] A. E. Djrbashian, A. O. Karapetyan, Integral inequalities between conjugate pluriharmonic functions in multydimensional domains, Izvestia Acad Nauk Armenii, (1988), 216-236

[7] A. E. Djrbashian, F. A. Shamoian, Topics in the Theory of \(A^p_\alpha\) Spaces, Leipzig, Teubner (1988)

[8] J. Ortega, J. Fàbrega, Hardy's inequality and embeddings in holomorphic Triebel- Lizorkin spaces, Illinois J. Math., 43 (4) (1999), 733-751

[9] J. Ortega, J. Fàbrega, Holomorphic Triebel-Lizorkin spaces, J. Funct. Anal., 151(1) (1997), 177-212

[10] W. Rudin, Function Theory in the Unit Ball of \(\mathbb{C}^{n}\), Seria Matematika, VINITI, New York (1980)
- Google Scholar

[11] S. V. Shvedenko, Hardy classes and related spaces of analytik functions in the unit disk, polydisc and unit ball, Seria Matematika, VINITI, Russian (1985)
- Google Scholar

[12] Z. Wu, Area operator on Bergman space, Sci. in China, Ser A., 49 (2006), 987-1008

[13] K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Graduate Texts in Mathematics, Springer-Verlag, New York (2005)
- Google Scholar