Compact Commutators of Calderón-Zygmund and Generalized Fractional Integral Operators with a Function in Generalized Campanato Spaces on Generalized Morrey Spaces

Abstract

We consider the commutators $[b,T]$ and $[b,I_{\rho}]$, where $T$ is a Calderón-Zygmund operator, $I_{\rho}$ is a generalized fractional integral operator and $b$ is a function in Campanato spaces with variable growth condition. It is known that these commutators are bounded on generalized Morrey spaces with variable growth condition. In this paper we discuss the compactness of these commutators.