Compactness of composition operators on bmoa

Proceedings of the American Mathematical Society

Volumn 127, Issue 9, 1999, Pages 2715-2725

  Smith, Wayne ^a  

^a UNIVERSITY OF HAWAII   (United States)

Author keywords

Bounded mean oscillation; Compact composition operators

Indexed keywords

EID: 22844455983     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-99-04856-x     Document Type: Article

References (16)

1. [ALXZ] Aulaskari, R., Lappan, P., Xiao, J. and Zhao, R., On α-Bloch spaces and multipliers of Dirichlet spaces, J. Math. Anal. Appl. 209 (1997), 103-121. MR 98e:30036
2. [AFP] Arazy, J., Fisher, S. D. and Peetre, J., Möbius invariant function spaces, J. Reine Angew. Math. 363 (1985), 110-145. MR 87f:30104
3. [Ba] Baernstein, A., Analysis of functions of bounded mean oscillation, Aspects of contemporary complex analysis, Academic Press, New York, 1980, pp. 3-36.
4. [BCM] Bourdon, P. S., Cima, J. A. and Matheson, A. L., Compact composition operators on BMOA, preprint.
5. [ESS] Essén, M., Shea, D.F. and Stanton, C.S., A value-distribution criterion for the class L log L, and some related questions, Ann. Inst. Fourier (Grenoble) 35 (1985), 127-150. MR 87e:30041
6. [G] Garnett, J.B., Bounded Analytic Functions, Academic Press, New York, 1981. MR 83g:30037
7. [J] Jarchow, H., Compactness properties of composition operators, preprint.
8. [MM] Madigan, K. and Matheson, A., Compact composition operators on the Bloch space, Trans. Amer. Math. Soc. 347 (1995), 2679-2687. MR 951:47061
9. [P] Pommerenke, Ch., Boundary Behavior of Conformal Maps, Springer-Verlag, New York, Berlin, 1992.
10. [Sh1] Shapiro, J.H., The essential norm of a composition operator, Annals of Math. 127 (1987), 375-404. MR 88c:47058
11. [Sh2] Shapiro, J.H., Composition Operators and Classical Function Theory, Springer-Verlag, New York, Berlin, 1993. MR 94k:47049
12. [Sm] Smith, W., Inner functions in the hyperbolic little Bloch class, to appear, Mich. Math. J.
13. p spaces, Analysis 17 (1997), 239-263. CMP 98:05
14. [St] Stephenson, K., Weak subordination and stable classes of meromorphic functions, Trans. Amer. Math. Soc. 262 (1980), 565- 577. MR 81m:30029
15. [Tj] Tjani, M., Compact composition operators on some Möbius invariant Banach spaces, Thesis, Michigan State University (1996).
16. [Ts] Tsuji, M., Potential Theory in Modern Function Theory, Chelsea, New York, 1959. MR 54:2990