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

Abstract

In this article, we show continuity of commutators of Calderón-Zygmund operators [b,T]\left[b,T] with BMO functions in generalized Orlicz-Morrey spaces MΦ,φ(Rn){M}^{\Phi ,\varphi }\left({{\mathbb{R}}}^{n}). We give necessary and sufficient conditions for the boundedness of the genuine Calderón-Zygmund operators TT and for their commutators [b,T]\left[b,T] on generalized Orlicz-Morrey spaces, respectively.

Keywords

• generalized orlicz-morrey spaces
• genuine calderón-zygmund operator
• commutator
• bmo
• 42b20
• 42b35
• 46e30