Weighted composition operators on the Bergman space

Journal of the London Mathematical Society

Volumn 70, Issue 2, 2004, Pages 499-511

  Čučković, Željko ^a   Zhao, Ruhan ^a  

^a UNIVERSITY OF TOLEDO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 7544229713     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024610704005605     Document Type: Article

References (28)

1. R. AULASKARI, D. A. STEGENGA and J. XIAO, 'Some subclasses of BMOA and their characterization in terms of Carleson measures', Rocky Mountain J. Math. 26 (1996) 485-506.
2. S. AXLER and D. ZHENG, 'Compact operators via the Berezin transform', Indiana. Univ. Math. J. 47 (1998) 387-400.
3. M. D. CONTRERAS and A. G. HERNÁNDEZ-DÍAZ, 'Weighted composition operators on Hardy spaces', J. Math. Anal. Appl. 263 (2001) 224-233.
4. C. COWEN and B. MACCLUER, Composition operators on spaces of analytic functions (CRC Press, Boca Raton, 1995).
5. p spaces (Academic Press. New York, 1970).
6. p', Canad. J. Math. 16 (1964) 721-728.
7. J. B. GARNETT, Bounded analytic functions (Academic Press, New York, 1981).
8. P. R. HALMOS, Measure theory, Graduate Texts in Mathematics 18 (Springer, New York, 1974).
9. W. W. HASTINGS, 'A Carleson measure theorem for Bergman spaces', Proc. Amer. Math. Soc. 52 (1975) 237-241.
10. K. HOFFMAN, Banach spaces of analytic functions (Dover, New York, 1988).
11. C. J. KOLASKI, 'Isometries of the weighted Bergman spaces', Canad. J. Math. 34 (1982) 910-915.
12. D. H. LUECKING, 'Forward and reverse Carleson inequalities for functions in Bergman spaces and their derivatives', Amer. J. Math. 107 (1985) 85-111.
13. D. H. LUECKING and K. ZHU, 'Composition operators belonging to Schatten ideals', Amer. J. Math. 114 (1992) 1127-1145.
14. B. MACCLUER and J. SHAPIRO, 'Angular derivatives and compact composition operators on the Hardy and Bergman spaces', Canad. J. Math. 38 (1986) 878-906.
15. B. MACCLUER and R. ZHAO, 'Essential norms of composition operators between Bloch type spaces', Rocky Mountain J. Math., to appear.
16. G. MIRZAKARIMI and K. SEDDIGHI, 'Weighted composition operators on Bergman and Dirichlet spaces', Georgian Math. J. 4 (1997) 373-383.
17. A. MONTES-RODRIGUEZ, 'Weighted composition operators on weighted Banach spaces of analytic functions', J. London Math. Soc. 61 (2000) 872-884.
18. J. MOORHOUSE, 'Compact differences of composition operators', Preprint.
19. S. OHNO and R. ZHAO, 'Weighted composition operators on the Bloch space', Bull. Austral. Math. Soc. 63 (2001) 177-185.
20. S. OHNO, K. STROETHOFF and R. ZHAO, 'Weighted composition operators between Bloch-type spaces', Rocky Mountain J. Math. 33 (2003) 191-215.
21. J. SHAPIRO, 'The essential norm of a composition operator', Ann. of Math. 125 (1987) 375-404.
22. W. SMITH, 'Composition operators between Bergman and Hardy spaces', Trans. Amer. Math. Soc. 348 (1996) 2331-2348.
23. W. SMITH, 'Inner functions in the hyperbolic little Bloch class', Michigan Math. J. 45 (1998) 103-114.
24. D. VUKOTIĆ, 'Pointwise multiplication operators between Bergman spaces on simply connected domains', Indiana Univ. Math. J. 48 (1999) 793-803.
25. J. XIA, 'On a proposed characterization of Schatten-class composition operators', Proc. Amer. Math. Soc., to appear.
26. K. ZHU, Operator theory in function spaces (Marcel Dekker, New York, 1990).
27. K. ZHU, 'Duality of Bloch spaces and norm convergence of Taylor series', Michigan Math. J. 38 (1991) 89-101.
28. K. ZHU, 'Schatten class composition operators on weighted Bergman spaces of the disk', J. Operator Theory 46 (2001) 173-181.