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A characterisation is given of bounded embeddings from weighted $L^2$ spaces on bounded intervals into $L^2$ spaces on the half-plane, induced by isomorphisms given by the Laplace transform onto weighted Hardy and Bergman spaces (Zen spaces). As an application necessary and sufficient conditions are given for the boundedness of truncated Hankel and Toeplitz integral operators, including the weighted case.

Laplace–Carleson Embeddings on Model Spaces and Boundedness of Truncated Hankel and Toeplitz Operators