1.Sección Departamental de Matemática Aplicada, Facultad de Estudios Estadísticos,Universidad Complutense de Madrid,Madrid,Spain;2.Departamento de Matemática Aplicada I, Escuela de Ingeniería Industrial,Universidad de Vigo,Vigo,Spain
Abstract:
We establish an analog for bilinear operators of the compactness interpolation result for bounded linear operators proved by Cwikel and Cobos, Kühn and Schonbek. We work with the assumption that \(T:(A_0+A_1) \times (B_0+B_1) \longrightarrow E_0+E_1\) is bounded, but we also study the case when this does not hold. Applications are given to compactness of convolution operators and compactness of commutators of bilinear Calderón–Zygmund operators.