COMPACTNESS CHARACTERIZATION OF CALDERÓN-ZYGMUND COMMUTATORS OF TYPE THETA ON GENERALIZED MORREY-LORENTZ SPACES

Abstract

In this paper, we characterize the compactness of the Calderón-Zygmund commutator of type theta  (see Definitions 1.3, 1.4 and 1.5 in Section 1) on generalized Morrey-Lorentz spaces (see Defintion 1.1). More precisely, we prove that if b is a vanishing BMO function, then the commutator [b, T] is a compact operator on generalized Morrey-Lorentz spaces. We also obtain a sufficient condition for a subset in generalized Morrey-Lorentz spaces to be strongly pre-compact.