Bounded composition operators on de Branges-Rovnyak spaces

We study bounded composition operators acting on de Branges--Rovnyak spaces from the viewpoint of reproducing kernel Hilbert spaces.Using kernel domination and Schur product techniques, we obtain sufficient conditions for the boundedness of composition operators between de Branges--Rovnyak spaces. This kernel-based approach also extends naturally to weighted composition operators, yielding boundedness results that generalize known results for model spaces and recover earlier work as special cases. This manuscript has been submitted for publication.