CHARACTERIZING THE COMPACTNESS 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 [],bT of type θ on generalized Morrey-Lorentz spaces (),nprϕM. More precisely, we prove that if ()nbCMO∈, which is the ()nBMO closure of ()ncC∞, then [],bT is a compact operator on (),nprϕM for all 1p<<∞ and 1r≤<∞.