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Boundedness, compactness and Schatten-class membership of weighted composition operators
The boundedness and compactness of weighted composition operators on the
Hardy space 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 are considered, and the results of Harper and Smith,
linking their properties to those of Carleson embeddings, are extended to this
situation.Comment: 12 page