Computational Methods and Function Theory 9 (2009), No. 1, 27--46
Copyright Heldermann Verlag 2009
Jussi Laitila
jlaitila@iki.fi , University of Helsinki, Department of Mathematics and Statistics, P. O. Box 68 (Gustaf Hällströmin katu 2b), FIN-00014 University of Helsinki, Finland.
Let ψ and φ be analytic functions on the unit disk D such that φ(D)⊂D. We characterize the boundedness and compactness of the weighted composition operators f → ψ·(foφ) on BMOA, the space of analytic functions on D that have bounded mean oscillation on ∂D, and its subspace VMOA. We also provide estimates for the norm of a weighted composition operator on BMOA and its essential norm on VMOA. Finally, we use the above results to show that boundedness or compactness of a weighted composition operator on BMOA implies its boundedness or compactness on the Bloch space B, respectively.
Keywords: Weighted composition operator, pointwise multiplier, composition operator, bounded mean oscillation.
MSC 2000: Primary 47B38; Secondary 30H05, 30D50.
[FullText-pdf (356 K)] [FullText-ps (588 K)]