Characterizations for the genuine Calderon-Zygmund operators and commutators on generalized Orlicz-Morrey spaces

In this article, we show continuity of commutators of Calderon-Zygmund operators [b, T] with BMO functions in generalized Orlicz-Morrey spaces M-F,M-f(R-n). We give necessary and sufficient conditions for the boundedness of the genuine Calderon-Zygmund operators T and for their commutators [b, T] on generalized Orlicz-Morrey spaces, respectively.