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

In this article, we show continuity of commutators of Calder & oacute;n-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 Calder & oacute;n-Zygmund operators T and for their commutators [b, T] on generalized Orlicz-Morrey spaces, respectively.

Automated summary

In this article, the continuity of commutators [b, T] of Calderón-Zygmund operators with BMO functions in generalized Orlicz-Morrey spaces M-F, M-f(R-n) is demonstrated. Necessary and sufficient conditions for the boundedness of the genuine Calderón-Zygmund operators T and their commutators [b, T] on generalized Orlicz-Morrey spaces are provided.