Products of differentiation, composition and multiplication from Bergman type spaces to Bers type spaces

Integral Transforms and Special Functions

Volumn 18, Issue 3, 2007, Pages 223-231

  Zhu, Xiangling ^a,b  

^a SHANTOU UNIVERSITY   (China)

^b JIAYING UNIVERSITY   (China)

Author keywords

Bergman type space; Bers type space; Composition operator; Differentiation operator; Multiplication operator

Indexed keywords

EID: 33947366885     PISSN: 10652469     EISSN: 14768291     Source Type: Journal    
DOI: 10.1080/10652460701210250     Document Type: Article

References (17)

1. Metzger, J.A., 1989, Bounded mean oscillation and Riemann surfaces. Bounded Mean Oscillation in Complex Analysis (Joensuu University), pp. 79-100.
2. Hedenmalm, H., Korenblum, B. and Zhu, K., 2000, Theory of Bergman spaces. Graduate Texts in Mathematics, 199 (New York: Springer-Verlag).
3. He, W. and Jiang, L., 2002, Composition operator on Bers-type spaces. Acta Mathematical Sciensia Series B England Edition, 22(3), 404-412.
4. Hu, Z., 2003, Extend Cesàro operators on mixed norm spaces. Proceedings of American Mathematical Society, 131(7), 2171-2179.
5. Shields, A.L. and Williams, D.L., 1971, Bounded projections, duality, and multipliers in spaces of analytic functions. Transactions of the American Mathematical Society, 162, 287-302.
6. Cowen, C.C. and MacCluer, B.D., 1995, Composition Operators on Spaces of Analytic Functions. Studies in Advanced Mathematics (Boca Raton: CRC Press).
7. Shapiro, J.H., 1993, Composition Operators and Classical Function Theory (New York: Springer-Verlag).
8. Zhu, K., 1990, Operator Theory in Function Spaces (New York and Basel: Marcel Dekker Inc).
9. Contreras, M.D. and Hernández-Díaz, A.G., 2001, Weighted composition operators on Hardy spaces. Journal of Mathematical Analysis and Applications, 263(1), 224-233.
10. Contreras, M.D. and Hernández-Díaz, A.G., 2003, Weighted composition operators between different Hardy spaces. Integral Equations Operator Theory, 46(2), 165-188.
11. Čučković, Ž. and Zhao, R., 2004, Weighted composition operators on the Bergman space. Journal of London Mathematical Society, 70(2), 499-511.
12. Li, S. and Stevič, S., 2007, Weighted composition operator from Bergman type space to α-Bloch spaces. Proceedings of Indian Academy of Science, in press.
13. Montes-Rodríguez, A., 2000, Weighted composition operators on weighted Banach spaces of analytic functions. Journal of London Mathematical Society, 61(3), 872-884.
14. Hibschweiler, R.A. and Portnoy, N., 2005, Composition followed by differentiation between Bergman and Hardy spaces. Rocky Mountain Journal of Mathematics, 35(3), 843-855.
15. Portnoy, N., 1998, Differentiation and composition on the Hardy and Bergman spaces, Dissertation, University of New Hampshire.
16. Ohno, S., 2006, Products of composition and differentiation between Hardy spaces. Bulletein of Australian Mathematical Society, 73(2), 235-243.
17. n (New York: Springer-Verlag).