Compactness characterization of commutators for Littlewood-Paley operators

Abstract

In this paper, the authors prove that the commutator [b,L] is a compact operator in L^p(Rⁿ) if and only if b ∈ VMO(Rⁿ), where L denotes the Littlewood-Paley operators, such as the Littlewood-Paley g-function, Lusin area integral and Littlewood-Paley g_λ^* function.