Boundedness, compactness and Schatten-class membership of weighted composition operators

Details Boundedness, compactness and Schatten-class membership of weighted composition operators Boundedness, compactness and Schatten-class membership of weighted composition operators

2009-07-14

arxiv.org/abs/0907.2370v1

Mathematics

Functional Analysis

12 pages

Scientific paper

The boundedness and compactness of weighted composition operators on the Hardy space ${\mathcal H}^2$ of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schatten-class membership is also considered; as a result, stronger forms of the two main results of a recent paper of Gunatillake are derived. Finally, weighted composition operators on weighted Bergman spaces $\mathcal{A}^2 \alpha(\mathbb{D})$ are considered, and the results of Harper and Smith, linking their properties to those of Carleson embeddings, are extended to this situation.

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