Trace ideal criteria for embeddings and composition operators on K_theta spaces

We will look at embeddings and composition operators on coinvariant subspaces of the Hardy space, so called model spaces. In particular we investigate the case in which the defining inner function is one-component, developing an extension process to reduce to the study of an equivalent embedding operator on a Hardy-Smirnov space of a different domain. From there we deduce criteria for embeddings and composition operators to be p-Schatten, obtaining characterizations that are in the spirit of previous work of Baranov and Luecking, Zhu. Based on joint work with Alexandru Aleman, Yura Lyubarskii, and Eugenia Malinnikova.