Compactness of the commutators of intrinsic square functions on weighted Lebesgue spaces

Abstract

The aim of this paper is to study the compactness for the commutators of intrinsic square functions, including the intrinsic $g_{\lambda}^*$-function and the intrinsic Littlewood-Paley g-function. Using a weighted version of the Frech\'{e}t-Kolmogorov-Riesz theorem, the compactness for their commutators generated with the CMO functions is obtained on the weighted Lebesgue spaces.