Abstract
Given a large weighted Hardy space we show there exists a composition operatorCϕ with ∥φ∥∞ that maps from that space into the unweighted Dirichlet space and lies in every Schatten p-class for 0<p<∞. This is in contrast to the situation in which the image space is a smaller weighted Dirichlet space. It is known that in that case it is not possible to find such a composition operator that is bounded.
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